VITEEE 2010 Paper

The given two circles are
2x2+2y2−3x+6y+k=0
⇒ x2+y2−

3

2

x+3y+

k

2

=0 ...(i)
and x2+y2−4x+10y+16=0...(ii)
Since, general equation of circle is
x2+y2+2‌gx+2‌fy+c=0...(iii)
Therefore, comparing eqs. (i) and (ii) with eq. (iii), we get
g1=−

3

4

,f1=

3

2

,c1=

k

2

and g2=−2,f2=5,c2=16
Both the circles cut orthogonally,
∴ 2(g1g2+f1f2)=c1+c2
⇒ 2(

3

2

+

15

2

)=

k

2

+16
⇒ 18=

k

2

+16
⇒

k

2

=2
⇒ k=4