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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

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Diameter makes an angle `theta` with x-axis.
So, the slope of diameter is `tan theta`

Let this diameter meet the circle at points A and B.
Thus, the coordinates of A and B are given by `(a+- r cos theta, b +- r sin theta)`
Therefore, equations of tangents at points A and B are given by
`(x-a)(a+-r cos theta-a) +(y-b)(b+-r sin theta -b)=r^(2)`
or `+-(x-a)cos theta +- r(y-b) sin theta =r`
or `(x-a)cos theta +(y-b) sin theta = +- r `
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