VITEEE 2016 Paper

Any tangent to parabola
y2 = 8x is y = mx +

2

m

... (i)
It touches the circle
x2+y2 - 12x + 4 = 0
if the length of perpendicular from the centre (6,0) is equal to radius
√32
∴

6m+ 2 m

√m2+1

= ± √32
⇒ (3m+

1

m

)2 = 8 (m2+1)
⇒ (3m2+1)2 = 8 (m4+m2)
⇒ m4−2m2 + 1 = 0 ⇒ m = ± 1
Hence, the required tangents are y = x + 2 and y = - x - 2.