Question 1 :
If the sum of the distance of a point <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7ba066f3020298ca1287d"> from two perpendicular lines in a plane is 1, then the locus of <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7ba066f3020298ca1287d"> is a

Question 2 :
A point on the parabola {tex} y ^ { 2 } = 18 x {/tex} at which the ordinate increases at twice the rate of the abscissa is

Question 3 :
If <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7bb2a6f3020298ca12b5c"> , then the points <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7bb2ac2a2ae2953d936a4"> and <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7ba54c2a2ae2953d9346c"> are

Question 4 :
Let {tex} A ( h , k ) , B ( 1,1 ) {/tex} and {tex} C ( 2,1 ) {/tex} be the vertices of a right angled triangle with {tex} A C {/tex} as its hypotenuse. If the area of the triangle is 1 square unit, then the set of values which {tex} ^ { \prime } k ^ { \prime } {/tex} can take is given by

Question 5 :
The feet of the perpendicular drawn from <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7ba066f3020298ca1287d"> to the sides of a <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7ba17ab3481716f4b61cc"> are collinear, then <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7ba066f3020298ca1287d"> is

Question 6 :
If the sum of the slopes of the lines given by {tex} x ^ { 2 } - 2 c x y - 7 y ^ { 2 } = 0 {/tex} is four times their product, then {tex} c {/tex} has the value

Question 7 :
The normal to the curve {tex} x = a ( 1 + \cos \theta ) , y = a \sin \theta {/tex} at {tex} \theta {/tex} always passes through the fixed point

Question 8 :
The equation of the straight line passing through the point {tex} ( 4,3 ) {/tex} and making intercepts on the coordinate axes whose sum is {tex} - 1 {/tex} is

Question 9 :
A parabola has the origin as its focus and the line {tex} x = 2 {/tex} as the directrix. Then the vertex of the parabola is at

Question 10 :
If {tex} \left( a , a ^ { 2 } \right) {/tex} falls inside the angle made by the lines {tex} y = \frac { x } { 2 } , x > 0 {/tex} and {tex} y = 3 x , x > 0 , {/tex} then {tex} a {/tex} belongs to

Question 11 :
If one of the lines of {tex} m y ^ { 2 } + \left( 1 - m ^ { 2 } \right) x y - m x ^ { 2 } = 0 {/tex} is a bisector of the angle between the lines {tex} x y = {/tex} {tex} 0 , {/tex} then {tex} m {/tex} is

Question 12 :
For the Hyperbola {tex} \frac { x ^ { 2 } } { \cos ^ { 2 } \alpha } - \frac { y ^ { 2 } } { \sin ^ { 2 } \alpha } = 1 , {/tex} which of the following remains constant when {tex} \alpha {/tex} varies?

Question 13 :
The equation of a tangent to the parabola {tex} y ^ { 2 } = 8 x {/tex} is {tex} y = x + 2 . {/tex} The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

Question 14 :
If the vertices of a triangle have integral coordinates, the triangle cannot be

Question 15 :
Circumcentre of triangle whose vertices are (0, 0), (3, 0) and (0, 4) is