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Stationary Point

A curve has e...

Question

A curve has equation $(x - 4)^{2} + (y + 1)^{2} = 36$ . If the origin is translated to $(4, - 1)$ , then the equation of the curve in translated system becomes $X^{2} + Y^{2} = K^{2}$ . Find the value of $K$ .

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Solution

Given the curve has equation $(x - 4)^{2} + (y + 1)^{2} = 36$
$∴$ The center = (4,-1) and radius=6
The orgin is transfered to (4,-1) i.e, to the centervof curve
$x^{2} = (x - 4)^{2}, y^{2} (y + 1)^{2} ∴ K^{2} = 36 ⟹ k = 6$

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