AP EAMCET Engineering 21 Apr 2019 Shift 1 Paper

Let (h,k) be the intersection point of tangent. Then the chord of the tangent is the common chord of the circles
x2+y2=12 and x2−y2−5x+3y−2=0
Consider the diagram,
The equation of the common chord is, 5x−3y−10=0
The equation of the common chord is,
5x−3y−10=0‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I)
The equation of common chord of contact is
hx+ky−12=0‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II)
The equation (I) and (II) represents the same line so,
‌

h

5

‌‌=‌

k

−3

‌‌=‌

−12

−10

This gives,
h=6,k=‌

−18

5

Hence the required point is (6,−‌

18

5

)