MEDIUM
JEE Advanced
IMPORTANT
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OA and OB are two mutually perpendicular chords of y2=4ax, O being the origin. Line AB will always passes through the point

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Important Questions on Parabola

MEDIUM
JEE Advanced
IMPORTANT
The length of latus rectum of the parabola, whose focus is asin2θ,acos2θ and directrix is the line y=a is
HARD
JEE Advanced
IMPORTANT
The point a,2a is an interior point of the region bounded by the parabola y2=16x and the double ordinate through the focus. Then, a belongs to the open interval
EASY
JEE Advanced
IMPORTANT
The vertex of a parabola y2=8x is at the centre of a circle and parabola cuts the circle at ends of its latus rectum. Then, equation of the circle is
HARD
JEE Advanced
IMPORTANT
AB is a chord of the parabola y2=4ax with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is
HARD
JEE Advanced
IMPORTANT
The circle x2+y2+2λx=0, λR, touches the parabola y2=4x externally. Then,
HARD
JEE Advanced
IMPORTANT
Vertex of the parabola whose parametric equation is x=t2-t+1, y=t2+t+1, tR, is
HARD
JEE Advanced
IMPORTANT
The circle x2+y2+2gx+2fy+c=0 cuts the parabola x2=4ay at point Aixi,yi, i=1, 2, 3, 4 then
HARD
JEE Advanced
IMPORTANT
A circle is drawn to pass through the extremities of latus rectum of the parabola y2=8x. It is given that this circle also touches the directrix of the parabola. Radius of this circle is equal to