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find the common tangents of the circle...

find the common tangents of the circle `x^2+y^2=2a^2` and the parabola` y^2=8ax`

Text Solution

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Standard equation of parabola is `y^2 = 4ax`
Here, equation of parabola is `y^2 = 8ax`
Thus, here `a = 2a`
Standard condition for tangency is `c = a/m`
As, here, `a = 2a`,
`:. c = (2a)/m`
Putting this value in, common equation of tangent, `y = mx+c`, it becomes
`y = mx+(2a)/m`
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