Question

Find the locus of poles of with respect to the parabola y² =ax
of the tangent
to the circle. x2 + y2 = 4a² ​

Answer 1

Answer:

Given parabola y

2

=4ax and hyperbola x

2

−y

2

=a

2

⇒

a

2

x

2

−

a

2

y

2

=1

Polar of point P (X,Y) wrt the given parabola is yY−2ax−2aX=0

Now the condition of tangency is a

2

l

2

−b

2

m

2

=n

2

Substitute values, we get

⇒a

2

4a

2

−a

2

Y

2

=4a

2

X

2

⇒4a

2

−Y

2

=4X

2

⇒4X

2

+Y

2

=4a

2