AP EAMCET Engineering 2012 Solved Paper

Given coaxial system of circle is
4x2+4y2−12x+6y−3 +λ(x+2y−6)=0
or x2+y2−3x+

3y

2

−

3

4

+

λ

4

(x+2y−6)=0
Here, radical axis is x+2y−6=0.
i.e., line of centre is
2x−y+k=0 ......(i)
Here, centre of circle is (

3

2

,−

3

4

) which lies on Eq. (i).
∴ 2(

3

2

)+

3

4

+k=0
⇒

12+3

4

+k=0
⇒ k=−

15

4

∴ Required equation is2x−y−

15

4

=0
⇒ 8x−4y−15=0