Parabola Questions

Let C be a circle and L a line on the same plane such that C and L do not intersect. Let P be a moving point such that the circle drawn with centre at P to touch L also touches C. Then the locus of P ...

Through the vertex O of the parabola, y2 = 4ax two chords OP and OQ are drawn and the circles on OP and OQ as diameter intersect in R. If θ1, θ2 and f are the angles made with the axis by th...

AB, AC are tangents to a parabola y2 = 4ax, p1 p2 and p3 are the lengths of the perpendiculars from A, B and C respectively on any tangent to the curve, then p2, p1, p3 are in-...

If the focus of the parabola (y - λ)2 = 4(x - λ) always lies between the lines 2x + y = 1 and 2x + y = 3 then the sum of all integral values of λ is -...

The equation of image of parabola x2 = 4y with respect to line mirror x - y + 2 = 0 is -

The line 2(x - a) + cy = 0 cuts the parabola y2 = 8x at P(2t12, 4t1) and Q(2t22, 4t2). If a∈ [2,4] and c ∈ R then t1t2 belongs to -...

The area bounded by the parabola x2 = 8y & the line x - 2y + 8 = 0 is -

If two tangents drawn from a point P to the parabola y2 = 4x be such that the slope of one tangent is double of the other, then P lies on the curve. :-

The co-ordinates of a point on the parabola y2 = 8x whose focal distance is 4 is

The equation of lactus rectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12, then length of L.R. is :-

A parabola passes through (1, 2) and (3, 4). The tangents drawn at these points intersect at (-6, 8), then the slope of directrix of the parabola is

The equation of a straight line passing through the point (3, 6) and cutting the curve y = √x orthogonally is -

Locus of the intersection of the tangents at the ends of the normal chords of the parabola y2 = 4ax is -

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x1, y1) and (x2, y2) respectively, then -...

The length of the chord of the parabola y2 = x which is bisected at the point (2, 1) is -

PQ is a normal chord of the parabola y2 = 4ax at P, A being the vertex of the parabola. Through P a line is drawn parallel to AQ meeting the x-axis in R. Then the length of of AR is -...

The straight line joining any point P on the parabola y2 = 4ax to the vertex and perpendicular from the focus to the tangent at P, intersect at R, then the equation of the locus of R is -...

Let PSQ be the focal chord of the parabola, y2 = 8x. If the length of SP = 6 then, i(SQ) is equal to(where S is the focus) -

If the tangent at the point P (x1, y1) to the parabola y2 = 4ax meets the parabola y2 = 4a (x + b) at Q & R, then the mid point of QR is -...

The co-ordinates of a point on the parabola 2y = x2 which is nearest to the point (0, 3) is