For all values of the parameter α, show that the locus of the point of intersection of the lines x cos α + y sin α =- p and x sin α − y cos α = q is the circle x2 + y2 = p2 + q2.

For all values of the parameter α, show that the locus of the point

1.	For all values of the parameter α, show that the locus of the point of intersection of the lines x cos α + y sin α =- p and x sin α − y cos α = q is the circle x2 + y2 = p2 + q2.
Answer» Squaring and adding the given equations, we have x² + y² = p² + q² which represents circle with centre as origin and radius √p² + q²

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For all values of the parameter α, show that the locus of the point of intersection of the lines x cos α + y sin α =- p and x sin α − y cos α = q is the circle x2 + y2 = p2 + q2.

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