Question

Prove that the tangents from (0 ,5) to the circle x^(2)+y^(2)+2x-4=0 & x^(2)+y^(2)y+1=0 are equal​

Answer 1

Answer:

Correct option is

A

2x−y+1=0, x+2y−2=0

Let equation of tangent with slope =m and point (0,1)

(y−1)=m(x−0)⇒y=mx+1

Intersection point

x

2

+(mx+1)

2

−2x+4(mx+1)=0

(1+m

2

)x

2

+(−2+6m)x+5=0

For y=mx+1 to be tangent, discriminant =0

(6m−2)

2

−4×5(1+m

2

)=0

36m

2

+4−24m−20m

2

+20=0

16m

2

−20m+24=0⇒2m

2

−3m−2=0

(2m+1)(m−2)=0

m=2,

2

−1

Equation of tangents

y=

2

−1

x+1⇒x+2y−2=0

and

y=2x+1⇒2x−y+1=0