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Equation of Circle with (h,k) as Center

Find the equa...

Question

Find the equation of circle on which the co-ordinates of any point are $(2 + 4 c o s θ, - 1 + 4 s i n θ), θ$ being the parameter.

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Solution

$x = 2 + 4 c o s$ $θ$ , $y = - 1 + 4 s i n θ$
clearly $(x - 2)^{2} + (y + 1)^{2}$
$= 16 (c o s^{2} θ + s i n^{2} θ) = 16$
Above represents a circle with centre $(2, - 1)$ and radius $4$

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