Question

Let $P(x_1,y_1)$ be a point lying inside or outside a given parabola. Suppose any straight line drawn through $P$ intersects the parabola at $Q$ and $R$. Then the locus of the point of intersection of the tangents to the parabola at $Q$ and $R$ is called the ______ of the given point $P$ w.r.t. the parabola and the point $P$ itself is called the _____ of the polar.

• A. (polar, director circle)
• B. (pole, director circle)
• C. (polar, pole)
• D. (director circle, pole)

Answer 1

Answer: (C)

(polar, pole)

The locus of the point of intersection of tangents drawn at the the end points of a variable chord through a fixed point P will be a straight line called polar of P and point P is called the pole of polar.

So, P is the fixed point here. Points Q and R are the end points of the chord through P.

So, by the definition of pole and polar, locus of point of intersection of tangents at Q and R is called the pole of point P w.r.t the parabola.

And point P is called the pole of the polar.

The answer is option (C).