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Conic Sections

Study point

Jan 25, 6:00 PM

60 minutes

Jan 29, 6:00 PM

40.0 marks

MCQ

20 questions

STUDY POINT CBSE ICSE

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Chemistry

Class Xi

Chemistry

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Question Text

Question 1 :
The lines $2x -3y=5$ and $3x -4y =7$ are the diameters of a circle of area $154$ square units. An equation of this circle is $(\pi = 22/7)$

Question 2 :
The equation of the circle having normal at $(3, 3)$ as $y = x$ and passing through $(2, 2)$ is:

Question 4 :
Find the latus rectum of the parabola $x^2\, +\, 2y- 3x\, +\, 5\, =\, 0$<br/>

Question 5 :
The equation of the circle passing through $(3, 6)$ and whose centre is $(2, -1)$ is

Question 7 :
If $(4,3)$ and $(-12,-1)$ are end points of a diameter of a circle, then the equation of the circle is-<br>

Question 8 :
A circle is concentric with circle $x^{2}+ y^{2}-2x+4y-20=0$. If perimeter of the semicircle is $36$ then the equation of the circle is :

Question 9 :
The order of the differential equation of the family of parabolas whose length of latus rectum is fixed and axis is the X-axis 

Question 10 :
Equation of the circle of radius 5 whose centre lies on y-axis in first quadrant and passes through$\left( {3,\,\,\,\,2} \right)$ is

Question 11 :
if the lines $ 3x-4y-7=0$ and $2x-3y-5=0$ are two diameter of a circle of area $49\pi$ square units the equation of the circle is

Question 12 :
The line segment joining the foci of the hyperbola $x^{2} - y^{2} + 1 = 0$ is one of the diameters of a circle. The equation of the circle is :

Question 13 :
If the tangent to the curve, $y=x^3+ax-b$ at the point $(1, -5)$ is perpendicular to the line, $-x+y+4=0$, then which one of the following points lies on the curve?

Question 14 :
The equation of the smallest circle passing through the points $(2, 2)$ and $(3, 3)$ is

Question 15 :
On the parabola $y={ x }^{ 2 }$, the point least distant from the straight line $y=2x-4$ is

Question 17 :
A parabola with axis parallel to $x$ axis passes through $(0, 0), (2, 1), (4, -1).$ Its length of latus rectum is<br/>

Question 18 :
Consider the parametric equation<br/>$x = \dfrac {a(1 - t^{2})}{1 + t^{2}}, y = \dfrac {2at}{1 + t^{2}}$.What does the equation represent?

Question 19 :
The radius of the circle passing through the point $(6, 2)$ and two of whose diameters are $\displaystyle x+y=6$ and $\displaystyle x+2y=4$ is:

Question 20 :
The equation of the circle having centre $(1,\ -2)$ and passing through the point of intersection of the lines $3x+y=14$ and $2x+5y=18$ is

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