MathDB

B.Stat & B.Math 2022 - Q3

Source: Indian Statistical Institute (ISI) - B.Stat & B.Math Entrance 2022

May 8, 2022

isiIndian Statistical Institutecoordinate geometry2022

Problem Statement

Consider the parabola

C: y^{2}=4 x

and the straight line

L: y=x+2

. Let

P

be a variable point on

L

. Draw the two tangents from

P

C

and let

Q_{1}

and

Q_{2}

denote the two points of contact on

C

. Let

Q

be the mid-point of the line segment joining

Q_{1}

and

Q_{2}

. Find the locus of

Q

P

moves along

L