Question

The angle between a pair of tangents drawn from a point p to the circle

Answer 1

Answer:

x2+y2+4x−6y+9=0

Step-by-step explanation:

Centre of the circle

x2+y2+4x−6y+9 sin2 α+13cos2 α=0

is C (-2,3) and its radius is

(−2)2+(3)2−9 sin2 α−13cos2 α−−−−−−−−−−−−−−−−−−−−−−−−−−−√

=13−13cos2 α−9sin2α−−−−−−−−−−−−−−−−−−−√

=13 sin2α−9sin2α−−−−−−−−−−−−−−−√=4sin2 α−−−−−−√=2sin α

Let (h,k) be any point Pand ∠APC= α,∠PAC=π/2

That is, triangle APC is a right angled triangle.

∴ sin α=ACPC=2sin α(h+2)2+(k−3)2√

⇒ (h+2)2+(k−3)2=4

⇒ h2+4+4h+k2+9−6k=4

⇒ h2+k2+4h−6k+9=0

Thus, required equation of the locus is

x2+y2+4x−6y+9=0