Consider A Parabola y2 = 4ax, The Length Of Focal Chord Is l and The Length Of The Perpendicular From Vertex To The Chord Is pthen

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Consider a parabola y2 = 4ax, the length of focal chord is l and the length of the perpendicular from vertex to the chord is pthen


Correct option is

l.p2 is constant

Let P(at2, 2at) and  be a focal chord of the parabola

(as t1t2 = –1)

Length of PQ =   




Length of the perpendicular from the vertex (0, 0) on the linePQ whose equation is

            is given by


So that       .

Which is constant.



The tangents at three points A, B, C on the parabola y2 = 4x, taken in pairs intersect at the points Pand R. If  be the areas of the triangles ABC and PQR respectively, then 


The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix


Equation of a common tangent to the curves y2 = 8x and xy = –1 is 


The tangent at the point P(x1y1) to the parabola y2 = 4ax meets the parabola y2 = 4a(x + b) at Q and R, the coordinates of the mid-point of QR are  


Tangent are drawn to a parabola from a point T. If P, Q are the points of constant then perpendicular distance from P, T and upon the tangent at the vertex of the parabola are in.


Chord of the parabola  which subtend right angle at vertex pass through


The locus of the vertex of the family of parabolas   is