Question

if the tangent to the parabola y^2=4ax meets the axis in t and the tangent at the vertex a in y and the rectangle tayq is completed prove that locus of q is parabola​

Answer 1

Answer:

Let P(at

2

,2at) be any point on the parabola y

2

=4ax.

The equation of tangent at P is ty=x+at

2

Since the tangent meets the axis of parabola in T and tangent at the vertex A in Y,

∴ coordinates of T and Y are (−at

2

,0) and (0,at) respectively.

Let the coordinate of G be (x

1

,y

1

)

Since TAYG is a rectangle,

∴ midpoint of diaginals TY and GA is same