Question

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.

Solution

Correct option is

G.P.

Let P(at2, 2at), (at22, 2at2), then the pint of intersection of the tangents t1y = x + at12  and t2y = x + at22 is T(at1t2a(t1 +t2)).

Distance of P, T and Q from y-axis, the tangent at the vertex areat2at1t2at22 which are G.P.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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  

Q4

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

Q5

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

Q6

The locus of the vertex of the family of parabolas   is