Question

Identify the correct statement(s) -

• A. In a parabola vertex is the mid point of focus and foot of directrix.
• B. $P \left( at _1^2, 2 at _1\right) \& Q \left( at _2^2, 2 at _2\right)$ are two points on $y ^2=4 ax$ such that $t _1 t _2=-1$, then normals at $P$ and $Q$ are perpendicular.
• C. There doesn't exist any tangent of $y^2=4 a x$ which is parallel to $x$-axis.
• D. At most two normals can be drawn to a parabola from any point on its plane.

Answer 1

Answer: (A), (B), (C)

Correct answer is (a) In a parabola vertex is the mid point of focus and foot of directrix.Correct answer is (b) $P \left( at _1^2, 2 at _1\right) \& Q \left( at _2^2, 2 at _2\right)$ are two points on $y ^2=4 ax$ such that $t _1 t _2=-1$, then normals at $P$ and $Q$ are perpendicular.Correct answer is (c) There doesn't exist any tangent of $y^2=4 a x$ which is parallel to $x$-axis.