A square has one vertex at the vertex of the parabola `y^2=4a x` and the diagonal through the vertex lies along the axis of the parabola. If the ends of the other diagonal lie on the parabola, the coordinates of the vertices of the square are `(4a ,4a)` (b) `(4a ,-4a)` `(0,0)` (d) `(8a ,0)`

Options

A. (4a,4a)
B. (4a,-4a)
C. (0,0)
D. (8a,0)

Answer

A, B, C

Explanation

AC is one diagonal along the x-axis. Then the other diagonal is BD, where both B and lie on the parabola. Also,

Slope of `AB="tan"(pi)/(4)=1`
If B is `(at^(2),2at)` then
Slope of `AB=(2at)/(at^(2))=(2)/(t)=1`
`:." "t=2`
Therefore, B is (4a,4a) and, hance, D is (4a,-4a).
Clearly, C is (8a,0).