AP EAPCET 18 May 2024 Shift 1 Solved Paper

We have, equation of two circlet
x2+y2+4x−5=0
and x2+y2−6y+8=0
Centre and radius of both circles are
‌c1=(−2,0,r1=√4+5=3.
‌c2=(0,3),r2=√9−8=1
Let P and Q be the internal and external centre of similitude, it divides C1C2 is ine ratio 3:1.
P=‌

x2+C1

3+1

=(‌

−2

4

,‌

9

4

)=(‌

−1

2

;‌

9

4

)
Here, a=‌

−1

2

and b=‌

9

4

Q=‌

3C2−C1

C1−C2

=(‌

2

2

,‌

9

2

)=(1,‌

9

2

)
Here, C=1 and d=‌

9

2

‌ Hence, ‌(a+∆)(b+c)‌=(‌

−1

2

+‌

9

2

)(‌

9

4

+1)\‌=‌

4×13

4

=13