MEDIUM
JEE Main/Advance
IMPORTANT
Earn 100

Let S is the focus of the parabola y2=4ax and X the foot of the directrix, PP' is a double ordinate of the curve and PX meets the curve again in Q. Prove that P'Q passes through focus.

Important Questions on Parabola

HARD
JEE Main/Advance
IMPORTANT
If x1, y1, x2, y2 and x3, y3 be three points on the parabola y2=4ax and the normals at these points meet in a point, then prove that x1-x2y3+x2-x3y1+x3-x1y2=0
HARD
JEE Main/Advance
IMPORTANT
A variable chord joining points Pt1 and Qt2 of the parabola y2=4ax subtends a right angle at a fixed point t0 of the curve. Show that it passes through a fixed point. Also find the co-ordinates of the fixed point.
HARD
JEE Main/Advance
IMPORTANT
Show that a circle circumscribing the triangle formed by three co-normal points passes through the vertex of the parabola and its equation is, 2x2+y2-2(h+2a)x-ky=0, where (h, k) is the point from where three concurrent normals are drawn.
HARD
JEE Main/Advance
IMPORTANT
If tangent drawn at a point t2,2t on the parabola y2=4x is same as the normal drawn at a point 5cosϕ,2sinϕ on the ellipse 4x2+5y2=20. Find the values of t & ϕ.