AP EAMCET Engineering 2018 Apr 23 Shift 2 Paper

Let the equation of tangent to parabola y2=x having slope m is,
y=mx+

1

4m

....(I)
For the common tangent to the circle,
x2+y2−6y+4=0 ....(II)
The radius is,
√9−4=

|3− 1 4m |

√1+m2

5(1+m2)=9+

1

16m2

−

3

2m

m=

1

2

So, the equation of the common tangent is,
y=

1

2

x+

1

2

x−2y+1=0