## Answers

Given that,

x = h + r cos(α)

i.e. r cos(α) = x - h.......... (1)

And,

y = k + r sin(α)

i.e. r sin(α) = y - k.......... (2)

.

Now by squaring and adding, both the equations, we get,

r^{2}cos^{2}(α) + r^{2}sin^{2}(α) = (x - h)^{2} + (y - k)^{2}

i.e.

R^{2}(cos^{2}(α) + sin^{2}(α)) = (x - h)^{2} + (y - k)^{2}

i.e. r^{2} = (x - h)^{2} + (y - k)^{2}

i.e. (x - h)^{2} + (y - k)^{2} = r^{2}

.

.

So the required rectangular equation is,

**(x - h) ^{2} + (y - k)^{2} = r^{2}**

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