TS EAMCET 20-July-2022 Shift 2 Solved Paper

Coordinate of D is (−5,4)
O is Mid-point of BD.
Let coordinate of B is (a,b)
⇒‌a−5/2=3 and b+4/2=−4
⇒‌‌a=11 and b=−12∴ Coordinate of B is (11,−12).
As AB|DC.
Equation of AB is y=−12
Coordinate of A is (−5,−12)
Equation of circle is
‌⇒(x−3)2+(y+4)2=128
‌⇒x2+y2−6x+8y−103=0
Tangent at point (−5,4) is
⇒−8x+8y−72‌=0
⇒x−y+9‌=0....(i)
Tangent at point (−5,−12)
⇒‌‌−8x−8y−136‌=0
x+y+17‌=0.....(ii)
Adding Eqs. (i) and (ii),
2x+26‌=0
x‌=−13
Substitute x=−13 in Eq. (i)
−13−y+9‌=0
y‌=−4
∴ The required point is (−13,−4).