Manipal Entrance Test 2020 Math Paper

Given system of circles is
x2+y2+4x+7=0.....(i)
2(x2+y2)+3x+5y+9=0
or ‌‌x2+y2+‌

3

2

x+‌

5

2

y+‌

9

2

=0 .....(ii)
and x2+y2+y=0......(iii)
The radical centre can be obtained by solving the Eqs. (i), (ii) and (iii).
On subtracting Eq. (ii) from Eq. (i), we get
4x−‌

3

2

x−‌

5

2

y+7−‌

9

2

=0
⇒‌‌‌

5

2

x−‌

5

2

y+‌

5

2

=0
⇒‌‌x−y+1=0....(iv)
On subtracting Eq. (iii) from Eq. (i), we get
4x−y+7=0‌‌...(v)
On solving Eqs. (iv) and (v), we get
x=−2 and y=−1
Hence, radical centre is (−2,−1).