Manipal Entrance Test 2015 Math Paper

The equation of any tangent to y2=8ax is
y=mx+

2a

m

...(i)
If it touches x2+y2=2a2, then
(

2a

m

)2=2a2(1+m2)
⇒2=m2(m2+1)
⇒m4+m2−2=0
⇒(m2+2)(m2−1)=0
⇒m2−1=0
⇒m=±1
we get Putting the values of m in Eq. (i), we get y=±(x+2a) as the equations of common tangents.