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Question
Find the equation of the straight lines passing through the following pair of point :
(a, b) and (a + c sin α, b + c cos α)
Solution
(a, b) and (a + csin α, b + ccos α)
\[\text { Here }, \left( x_1 , y_1 \right) \equiv \left( a, b \right) \]
\[\left( x_2 , y_2 \right) \equiv \left( a + c\sin\alpha, b + c\cos\alpha \right)\]
So, the equation of the line passing through the two given points is
\[y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}\left( x - x_1 \right)\]
\[ \Rightarrow y - b = \frac{b + c\cos\alpha - b}{a + c\sin\alpha - a}\left( x - a \right)\]
\[ \Rightarrow y - b = \cot\alpha\left( x - a \right)\]
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