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Per ee, , , , CONICS — Parabola,, Ellipse & Hyperbola, , , , Ifthe latus rectum ofan ellipse is equal to one half its minor, , , , , , , , , , , , , , , , , , , , x, , a, , =1_. What is the ratio ofa to b?, [2009-11], , ellipse, , , , @) 5/3 () 135, (©) 78 (@) 37, , ©, , , , axis, what is the eccentricity of the ellipse ? 8 Inhow many points do the ellipse =I and the circle, w@ 8 o B x? + =9 intersect ? (2007-1), a 2 (a) One () Two, (©) Four (@ None of the above, 3 vis, oF @ 2 [2006-1] . F, 9. Ifthe foci of the conics 5 hand G35, 2 P(2,2)isa point on the parabola y? = 2x and A is its vertex. a, Q is another point on the parabola such that PQ is were to coincide, then what is the value ofa? —/2007-I1], perpendicular to AP, What is the length of PQ? @ 2 &) 3, © 4 @ 16, @® 2 @) 22 10. Which one of the following is correct? The eccentricity of, © 42 (@) 6v2 [2006-1] the conic, 3. The focal distance of a point on the parabola y2= 12x is 4 w, What is the abscissa of the point ? oe = 1,020) 2008-1], @ 1 (bo) -1 ah+h bo+n, wal @ +2 pees (@) increases with increase in 4,, : i (b) decreases with increase in 4,, 4, If (2, 0) is the vertex and the y-anis is the directrix of a, parabola, then where is its focus ? (c) does not change with 2,, @ 0) ©) 62.0 (0), Note ctihentove, © 4,0) (d) 4,0) [2006-1], 5. Which one of the following points lies outside the ellipse 11. Consider the ellipse 7 1(6> a). Then, which one, 2g) aya, G2 fa?) + (7 /b7=1? of the following is correct? [2008-11], @ @o Oe) (@) Real foci donotexist (b) Fociare (+e, 0), ©) (a,0) @ (a,b) (2006-11) (©) Fociare(ebe,0) —(d)_- Fociare(0, be), 6 What is the equation of the parabola, whose vertex and f, focus are on the x-axis at distance a and b from the origin 12. Consider the parabolas 5, = y* ~4ax=0 and, respectively? (b >a>0) (2007-1) = 5 5‘, (@ y=8(b-a)(x-2) (0) y2=4b+aN xa) S, = y? ~4bx = 0. S, will contain S;, if [2008-1], (o) P=4(b—a)(xta) — (@)_ P= 4(b-ay(x—a) (@) a>b>0 () b>a>0, 7. Ifthe eccentricity and length of latus rectum of a hyperbola © 4>0,b<O0butp|>a () a<0,b>0butb>[a|, ie 13, Equation of the hyperbola with eccentricity 3/2 and foci at, % 0 (£2, 0)is Sx?—4y?= 2, Whats the value of k? [2008-11], <> and > ly, then wh k, are ~~ and units respectively, then what is the length eB ou, is? 2007-1, of the transverse axis’ 2007-1] © Was @ GOs, eo Cea () 12unit 14, What is the eccentricity of an ellipse, if its latusrectum is, 2 ‘equal to one-half of its minor axis? [2009-1], 6. i. (a) V4 & 12, © > wnit (J wnit © 514 @ 52, maya NDA Topicwise Solved Papers - MATHEMATICS, 15. What is the sum of focal radii of any point on an ellipse 24. A point P moves such that the difference of its, equal to? 2009-1] distances from two given points (c, 0) and(-<, 0) is constant., (a) Length of atusrectum ‘What is the locus of the point P? 2010-1], (b) Length of major-axis (2) Circle (b) Ellipse, (©) Length ofminor-axis (©) Hyperbota @_ Parabola, (@)_ Length ofsemi-latusrectum 25, Ifthe latusrectum of an ellipse is equal to halfits minor axis,, 16. What does an equation of the first degree containing one then what is its eccentricity? (2010-1,, arbitrary parameter passing through a fixed point represent? f, [2009-1] @ 5 ® 3, @ Circle (b) Straightline, (©) Parabola (@)_ Ellipse & 1, 17. The curve y?=—4ax (a> 0) lies in (2009-11) o> @® FB, (a) First and fourth quadrants . | ., (W) First and second quadrants 26. What are the points of intersection of the curve, (©) Second and third quadrants 4x? 9)? = | with its conjugate axis? PO1-l], (@) Third and fourth quadrants (@) (1/2,0)and(-12,0) (b) (0,2)and(0,~2), 2 (©) (0,3)and(0,-3) (4) Nosuch point exists, 18 The ellipse ~—+2—=1has the same eccentricity as the 27. What is the sum of the focal distances of a point of an, 169 * 25, , 2011-9

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LO: Peat | Per ee, , , , , , eae, ellipse “>, (2009-11), (@) Sn3 &) 135, © 78 (@) 87, , 19, If (4,0) and (-4,0) are the foci of an ellipse and the semi‘minor axis is 3, then the ellipse passes through which one of, , the following points? (2010-1), @ Go ©) @5), © 09) @ (50), , 20. What is the locus of points, the difference of whose, distances from two points being constant? —_/20/0-I), (a) Pairofstraight lines (b) Anellipse, (©) Abyperbola (@) Aparabola, , 2 a, au Acirle is drawn with the two fi ofan ellipse 75 + =1, a’, , at the end of the diameter. What is the equation of the circle?, (2010-1), @ P+y=a2+h ) P+ P=0-P, (0) x2+y7=2a2+) A) x2 +y? = 20a?), 22 What are the equations of the directrices of the ellipse, , , , 25x? + 16y?= 4007 ‘(2010-1], a) 3xt25=0 (b) 3yt25=0, © xt15=0 @ y225=0, , a yt, , , , 23, LetEbethecllipse “5+ -=LandCbethecirelex? +y?=9, Let, P= (1,2) and Q = (2, 1). Which one of the following is, ‘correct? (2010-1), (2) Qlies inside C but outside &, , (b) Olies outside both Cand £, (©) Plies inside both Cand E, (d) Plies inside C but outside £., , CONICS ~ Parabola, Ellipse & Hyperbola, , , , 2 2, llipse +25 =1? 201-1, ellipse 23 +73 PO1-], @)a (bo) 6, (©) 2 (d) 2, , Whaat is the area of the triangle formed by the lines joining, the vertex of the parabola x? = 12y to the ends of the latus, , , , rectum? (2011-1), (a) 9 square units (b) 12 square units, (©) 14 square units (@)_ 18 square units, 29. What is the focal distance of any point P(x), ¥4) on the, parabola y? = 4ax? [2011-1], @ x+y © xy, © ax, @ atx,, 30. Ifthe latus rectum of an ellipse is equal to half of the minor, axis, then what is its eccentricity? [2012-1], & A., © F oF, 5 1, © a OF, 31, What is the eccentricity of the conic 4x? + 9y?= 144?, 5 &, ® > ® > 2012-1], Be 2, oF @ 5, 32. The sum of the focal distances of a point on the ellipse, i, ae z, ey [2012-1], (a) 4units (b) 6 units, (©) Sunits (@) 10units, M175, , , , 33. The eccentricity e of an ellipse satisfies the condition:, , , , , , 2012-11], , @ e<o0 (b) 0<e<1, © e=1 (d) e>I, , 34, The equation of the ellipse whose vertices are (# 5, 0) and, foci at(#4,0)is 2013-1], @, , a 2 ¥, , © 6 @ 35 er, , 35. Thedifference of focal distances of any point on a hyperbola, is equal to 2013-1], (@ latusrectum (b)_ semi-transverse axis, (©) transverse axis (@), semi-latusrectum, , 36 The foci of the hyperbola 4x?—9?—1=Oare [2013-11], , VB, @ (ViB0) ) («Be, v3, , © (x2 (d)_ None of these, , 37, Theaxis of the parabola} + 2x=0is [2013-1], f@) ), © @, , , , 38. What is the sum of the major and minor axes of the ellipse, whose eccentricity is 4/5 and length of latus rectum is 14.4, , unit? Oi], (a) 32units (b) 48 units, ( 64units (d) None of these, IS (Qs. I-A: For the next wo (0D) ems tha, op, Comsideranelipse 75-455 =| [2014-1], a, 39, Whatis the area of the greatest rectangle that can be inscribed, in the ellipse?, @ ab (b) 2ab, (© abi2 @) Jab, , 40. Whatis the area included between the ellipse and the greatest, , a @, , DIRECTIONS (s. 43-45) : For the next three (03) items that, follow:, The line 2y = 3x + 12 euts the parabola 4y = 3x7 (2014-1), 43. Where does the line cut the parabola ?, (a) At(-2,3)only, (bo) At(4, 12) only, (©) Atboth (-2, 3) and (4, 12), (d)_ Neither at (-2, 3) nor (4, 12), 44. What is the area enclosed by the parabola and the line ?, (a) 27 square unit (b) 36square unit, (©) 48square unit (@) 54square unit, 45. What isthe area enclosed by the parabola, the line and the ¥=, axis in the first quadrant ?, , (a) 7 square unit (b) 14 square unit, (©) 20square unit (@ 21 square unit, , 46. ‘The point on the parabola y?=dax nearest to the focus has, its abscissa (2015-1), @) x=0 (b) x=a, © x85 (@ x=20, , , , 2 72, 47. The hyperbola 7-2—=1 passes through the point, a, , 2g?, , (3V5,1) and the length of its latus rectum is : units, The, , ength of the conjugate axis is 2015-1], (a) 2units (b) units, (©) 4units (@) Sunits, , 29, 48 Consider any point Pon the ellipse = +75, , , in the first, , quadrant. Let r and s represent its distances from (4,0) and, (4,0) respectively, then (r+s)isequal to (2005-II], , (@) 10unit (b) Suni, (© 8unit @ 6unit, 49. The eccentricity of the hyperbola 16x?— 9y= | is, 2015-11], , 3 5, , @ 5 Og, 4 5, , OF @ 4, , 50. What is the equation of the hyperbola having latus rectum, , <

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(@) Jab, , , , , , , , , 4 5, @ = OG, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , (©) abn =, 40, Whats thearea included between the ellipse and the greatest 50, What is the equation of the hyperbola having latus rectum, rectangle inseribed in the ellipse? z, (a) ab(x—1) (db) 2ab(x—1) and eccentrieity 8 and respectively? [2016-1], (©) ab(x-2) (qd) None of these, 41. What is the equation of parabola whose verted is at (0, 0) a ® sae, and focus is at (0,2)? 40, (@) 9 +8e @) yP-8x=0 2, (© +8 (@ *-8)=0 © DD Oo, 42, What is the length of the latus rectum of the ellipse 51 ihe ellipse 9x? “, 3 lipse 9x2 + 16y2= 14 intercepts the line 3x + 4y=12,, 2, 25x? + 16y?=400? (2014-1) then what is the length of the chord so formed? /20/6-11], a) 252 (b) 25/4 (a) Sunits (b) Gunits, () 165 (a) 325 (c) Sunits (d) 10units, M176 NDA Topicwise Solved Papers - MATHEMATICS, 52, Whats the eccentricity of rectangular hyperbola? [2016-1] ©) outside the pee, @ V2 © (0) inside the ellipse but not at the focus, © VS @ Je (©) onthe ellipse, DIRECTIONS (Os. 53-54) : Consider the following Jor the next (d)_ at the focus, ‘v0 (02) items that follow. 58, ‘The equation of the ellipse whose centre is at origin, major, ic 1 2 aK + a, — Paabolny pet ese 2end Weatnlentline axisis along x-axis wth eccentricity + and latus rectum 4, =, $3. What are the coordinates of the point on the parabola which units is (2017-1], is closest to the straight line? [2016-11] 2 2 a ae, 7 4s 7, @ 02) © (2,-8) o ae wo ee, ©) 2) (@) (1,10), ‘SA, What is the shortest distance from the above point on the a2 A9y2 2, parabola to the line? (2016-11) © wee @ +O, it io 1024 64 1024 64, a a= 59, What is the equation of the ellipse whose vertices are, 2 > (5,0) and foci are at (+4, 0)? 2018-1], 1 & 12, © Yo Oy @ & oe, 5S. What is the equation of the ellipse having foci (42, 0) and, 2 2, y’, the eccentricity ra [2017-4] © © Ts, 60. The sum of the focal distances of @ point on an ellipse is, x yt x2 ‘constant and equal to the (2019-1), ® Gta ) Oo (a) length of minor axis, (b) length of major axis, x Fr (c) length oflatus rectum, © Dh @ (@) sum ofthe lengths of semi-major and semi-minor axes, i 2 3y 2019-1, 56 Aman running round a racecourse notes that the sum of abies aS aye © tcl Buel, the distances of two flag-posts from him is always 10 mand © ancllipse (@ a hyperbola, the distance between the flag-posts is 8m. The area of the 6 The two parabolas y= dax and x?= day intersect, path he encloses is (2017-1, 2019-1), () Issuare mites, §— (0) LSiracaare metres (@) attwo points on the line y =x, (©) I2msquaremetres (4) 8 square metres i) oobatieseios, 57. The position of the point (1, 2) relative to the ellipse (attics points one wich lion yO, , 2x2+ Ty=20is [2017-1], , (@) onlyat (4a, 4a), , , , @