Is a variable on the line

MATHEMATICS · Subjective · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

P

is a variable on the line

y = 4

. Tangents are drawn to the circle

x^2 + y^2 = 4

from

P

to touch it at

A

and

B

. The parallelogram

PAQB

is completed. Find the equation of the locus of

Q