HARD
JEE Main
IMPORTANT
Earn 100

Show that all chords of a parabola which subtend a right angle at the vertex pass through a fixed point on the axis of the curve.

Important Questions on Conic Section

MEDIUM
JEE Main
IMPORTANT
Show that the locus of the foot of the perpendicular from the focus on the tangent at any point of the parabola is the tangent at the vertex.
EASY
JEE Main
IMPORTANT
Find the locus of the point of intersection of the normals to the parabola y2=4ax at the extremities of a focal chord.
EASY
JEE Main
IMPORTANT
If the sum of the tangents of the base angles of a triangle described on a given base be constant, show that the locus of its vertex is a parabola.
EASY
JEE Main
IMPORTANT
Prove that the locus of the centres of equilateral triangles inscribed in the parabola y2=4ax is 9y2=4ax-8a.
EASY
JEE Main
IMPORTANT
If the tangents at the points P and Q on the parabola y2=4ax meet at R and S is its focus, prove that SR2=SP. SQ.
EASY
JEE Main
IMPORTANT
The eccentricity of an ellipse is 12 and the distance between its foci is 4 units. If the major and minor axes of the ellipse are respectively along the x and y axes, find the equation of the ellipse.
MEDIUM
JEE Main
IMPORTANT
Find the equation to the ellipse (referred to its axes as the axes of x and y respectively) which passes through the point (-3,1) and has eccentricity 25
HARD
JEE Main
IMPORTANT
Find the latus rectum, eccentricity, coordinates of the foci and the length of axes of the ellipse 4x2+9y2-8x-36y+4=0