Question

if a tangent at any point on paradola y2=4ax intersect x-axis at T and y-axis at G and rectangle TAGI is completed then the locus of i will be , where A is the vertex of parabola-

a . y2+ax=0 

b. y2+2ax

c. x+ay2=0

d, x2+ay

Answer 1

The given parabola is y2 = 4ax.

Vertex of the parabola = A (a, 0)

Let the locus of I be (h, k).

So use eq. of tangent to parabola....

then u get
T=(-a/m2,0)

Substitute the values....

then you get the coordinates and thus the vertex of parabola is:-

Replacing h by x and k by y, we get y2 + ax + a2= 0

Thus, the required locus of I is y2 + ax + a2 = 0.