Question

find the angle between(1,3)to the circle x²+y²-2x+4y-11=0​

Answer 1

Answer:

We have, S=x

2

+y

2

−2x+4y−11=0

And the given point is (1,3)

So S

1

=(1)

2

+(3)

2

−2(1)+4(3)−11=9

and T=x(1)+y(3)−(x+1)+2(y+3)−11=5y−6

So equation of pair of tangent is given by, SS

1

=T

2

⇒9(x

2

+y

2

−2x+4y−11)=(5y−6)

2

⇒9x

2

+9y

2

−18x+36y−99=25y

2

−60y+36

⇒9x

2

−16y

2

−18x+96y−135=0

Comparing with general second degree equation,

a=9,b=−16,h=0

Thus angle between the tangents =tan

−1

∣

∣

∣

∣

∣

∣

a+b

h

2

−ab

∣

∣

∣

∣

∣

∣

=tan

−1

7

12