AP EAMCET Engineering 26 Apr 2017 Shift 1 Paper

The equation of tangents to the ellipse can be rewritten as,
y=2xw+√76
Its slope is
m1=2
And,
y=−

1

2

x+4
Its slope is,
m2=−

1

2

So,
m1×m2=2×(

−1

2

)
=−1
The tangents are perpendicular to each other.
Hence, the required circle is,
x2+y2=a2+b2
x2+y2=16+12
x2+y2=28