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Find the equation of the common tangents...

Find the equation of the common tangents to `y^2 = 8ax` and `x^2 + y^2 = 2a^2`

Text Solution

Verified by Experts

The correct Answer is:
`xpmy+2a=0`

The equation of tangent to the parabola `y^(2)=8ax` having slope m is
`y=mx+(2a)/(m)` (1)
the equation of tangent to the circle `x^(2)+y^(2)=2a^(2)` having slope m is
`y=mxpmsqrt(2a)sqrt(1+m^(2))` (2)
Equation (1) and (2) are identical. Therefore,
`(2a)/(m)=pmsqrt(2)asqrt(1+m^(2))`
`orm^(4)+m^(2)-2=0`
`or(m^(2)+2)(m^(2)-1)=0`
`orm^(2)-1=0`
`orm=pm1`
Hence, the required tangents are `x+y+2a=0`.
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