Two common tangents to `x^(2) + y^(2) = 2a^(2)` and `y^(2) = 8ax` are

Options

A. `x=+-(y+2a)`
B. `y=+-(y+2a)`
C. `x=+-(y+a)`
D. `x=+-(x+a)`

Answer

B

Explanation

The equation of any tangent to `y^(2)=8ax` is
`y=mx+(2a)/m" ..(1)"`
If touches `x^(2)+y^(2)=2a^(2),`
`((2a)/m)^(2)=2a^(2)(1+m^(2))" "["Using "c^(2)=a^(2)(1+m^(2))]`
`rArr" "2-m^(2)(m^(2)+1)`
`rArr" "m^(4)+m^(2)-2=0`
`rArr" "(m^(2)+2)(m^(2)-1)=0rArrm^(2)-1=0rArrm=+-1`
Pultting the values of m in (i), we get
`y = +-(x+2a)` as the equations of common tangents.