Identify the correct statement(s) -

Question

Identify the correct statement(s) - (A) In a parabola vertex is the mid point of focus and foot of directrix. (B) P ( at 12, 2 at 1) Q ( at 22, 2 at 2) 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 y2=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.

Tardigrade Admin · Accepted Answer

Correct answer is (a) In a parabola vertex is the mid point of focus and foot of directrix.Correct answer is (b) P ( at 12, 2 at 1) Q ( at 22, 2 at 2) 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 y2=4 a x which is parallel to x-axis.

Q. Identify the correct statement(s) -

In a parabola vertex is the mid point of focus and foot of directrix.

$P (a t_{1}^{2}, 2 a t_{1}) & Q (a t_{2}^{2}, 2 a t_{2})$ are two points on $y^{2} = 4 a x$ such that $t_{1} t_{2} = - 1$ , then normals at $P$ and $Q$ are perpendicular.

There doesn't exist any tangent of $y^{2} = 4 a x$ which is parallel to $x$ -axis.

At most two normals can be drawn to a parabola from any point on its plane.

Q. Identify the correct statement(s) -

In a parabola vertex is the mid point of focus and foot of directrix.

P(at12​,2at1​)&Q(at22​,2at2​) are two points on y2=4ax such that t1​t2​=−1, then normals at P and Q are perpendicular.

There doesn't exist any tangent of y2=4ax which is parallel to x-axis.

At most two normals can be drawn to a parabola from any point on its plane.

$P (a t_{1}^{2}, 2 a t_{1}) & Q (a t_{2}^{2}, 2 a t_{2})$ are two points on $y^{2} = 4 a x$ such that $t_{1} t_{2} = - 1$ , then normals at $P$ and $Q$ are perpendicular.

There doesn't exist any tangent of $y^{2} = 4 a x$ which is parallel to $x$ -axis.