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Find the slope of a common tangent to th...

Find the slope of a common tangent to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and a concentric circle of radius `rdot`

Text Solution

Verified by Experts

The correct Answer is:
`sqrt((r^(2)-b^(2))/(a^(2)-r^(2)))`
The equation of any tangent to the given ellipse is `y=mx+sqrt(a^(2)m^(2)+b^(2))`
If it touches `x^(2)+y^(2)=r^(2)`, then
`sqrt(a^(2)m^(2)+b^(2))=r sqrt(1+m^(2))`
or `m^(2)(a^(2)-r^(2))=r^(2)-b^(2)`
or `m=sqrt((r^(2)-b^(2))/(a^(2)-r^(2)))`
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