TS EAMCET 5 May 2018 Shift 2 Solved Paper

Consider the equation of circles.
x2+y2−14x+6y+33=0
Its centre is (7,-3) and radius is r1=5 .
And,
x2+y2+30x −2y+1=0
Its centre is (-15,1) and radius is r2=15
The point C1 that divides the center of circle externally in the ratio 1: 3 is calculated as,
C1=(

−15+21

4

,

1−9

4

)
=(

3

2

,−2)
The point C2 that divides the center of circle externally in theratio 1: 3 is calculated as,
C2=(

−15−21

1−3

,

1+9

1−3

)
=(

−36

−2

,

10

−2

)
=(18,−5)
Now, the equation of circle with diameter as C1C2 is given by,
(x−

3

2

)(x−18)+(y+2) (y+5)=0
2x2−36x−3x+54+2y2 +14y+20=0
2x2+2y2−39x +14y+74=0