MEDIUM
JEE Main
IMPORTANT
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If the x-intercept of a focal chord of the parabola y2=8x+4y+4 is 3, then the length of this chord is equal to _____ .

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Important Questions on Parabola

MEDIUM
JEE Main
IMPORTANT
If a line along a chord of the circle 4x2+4y2+120x+675=0, passes through the point (-30,0) and is tangent to the parabola y2=30x, then the length of this chord is:
MEDIUM
JEE Main
IMPORTANT
The locus of the mid points of the chords of the hyperbola x2-y2=4, which touch the parabola y2=8x, is :
MEDIUM
JEE Main
IMPORTANT
A tangent and a normal are drawn at the point P(2,-4) on the parabola y2=8x, which meet the directrix of the parabola at the points A and B respectively. If Q(a, b) is a point such that AQBP is a square, then 2a+b is equal to
EASY
JEE Main
IMPORTANT
If two tangents drawn from a point P to the parabola y2=16(x-3) are at right angles, then the locus of point P is:
EASY
JEE Main
IMPORTANT
The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S(>R) respectively from the origin, is :
MEDIUM
JEE Main
IMPORTANT
A tangent line L is drawn at the point 2, -4 on the parabola y2=8x. If the line L is also tangent to the circle x2+y2=a2, then a is equal to                       .
EASY
JEE Main
IMPORTANT
Consider the parabola with vertex 12, 34 and the directrix y=12. Let P be the point where the parabola meets the line x=-12. If the normal to the parabola at P intersects the parabola again at the point Q. then (PQ)2 is equal to :
HARD
JEE Main
IMPORTANT
Let the tangent to the parabola S:y2=2x at the point P2,2 meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to: