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Question

Find the equation to the tangent at A to the circle (xa)2+(yb)2=r2, where the radius through A makes an angle α with the xaxis.

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Solution

Coordinate of point A=(a+rcosα,b+sinα)
Also since AOD=α
ADO=90α
Slope of tangent =tan(90α)
=cotα
Equation of tangent,
y(b+rsinα)=cotα(x(a+rcosα)
ybrsinα=cotα(x)+cotα(a+rcosα).

1063852_1152462_ans_88d4e18c93014a73866d77aed102fea4.png

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