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Find the equation of the tangent at the ...

Find the equation of the tangent at the endpoints of the diameter of circle `(x-a)^2+(y-b)^2=r^2` which is inclined at an angle `theta` with the positive x-axis.

Text Solution

Verified by Experts

Diameter makes an angle `theta` with x-axis.
So, the slope of diameter is `tan theta`
Therefore, slope of tangent is `-cot theta`.
Hence, equations of tangents having slope `'-cot theta'` are given by
`y-b=- cot theta (x-a)+- r sqrt(1+cot^(2)theta)`
or `cos theta (x-a)+sin theta(y-b)= +- r`
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