The endpoints of two normal chords of a parabola are concyclic. Then the tangents at the feet of the normals will intersect at
a. Tangent at vertex of the parabola
b. Axis of the parabola
c. Directrix of the parabola
d. None of these

Options

A. tangent at vertex of the parabola
B. axis of the parabola
C. directrix of the parabola
D. none of these

Answer

B

Explanation

(2) Let the concyclic points be `t_(1),t_(2),t_(3), and t_(4)` Then,
`t_(1)+t_(2)+t_(3)+t_(4)=0`
Here, `t_(1)andt_(3)` are the feet of the normal. So,
`t_(2)=-t_(1)-(2)/(t_(1))andt_(4)=-t_(3)-(2)/(t_(3))`
`:.t_(1)+t_(2)=-(2)/(t_(1))andt_(4)+t_(3)=-(2)/(t_(3))`
Therefore, the lies on the intersection of tangents of tangents at `t_(1)andt_(3)` is `(at_(1)t_(3),a(t_(1)+t_(3)))-=(at_(1)t_(3),0)`.
This point lies on the axis of the parabola.