Let be the diameter of the circle

MATHEMATICS · Single correct · CBSE · Mathematics · Circles · Circles

Problem

Let

RS

be the diameter of the circle

x^2 + y^2 = 1

, where

S

is the point

(1, 0)

. Let

P

be a variable point (other than

R

and

S

) on the circle and tangents to the circle at

S

and

P

meet at the point

Q

. The normal to the circle at

P

intersects a line drawn through

Q

parallel to

RS

at point

E

. Then the locus of

E

passes through the point(s) (1)

\left(\frac{1}{3}, \frac{1}{\sqrt{3}}\right)

(2)

\left(\frac{1}{4}, \frac{1}{2}\right)

(3)

\left(\frac{1}{3}, -\frac{1}{\sqrt{3}}\right)

(4)

\left(\frac{1}{4}, -\frac{1}{2}\right)