Please solve question no.31.

Dear Student.

$$\begin{gathered} Given, x=h+a\cos \theta and y==k+a\sin \theta \\ Putting these values in {(x-h)}^2+{(y-k)}^2, we get: \\ {(h+a\cos \theta -h)}^2+{(k+a\sin \theta -k)}^2=(a\cos \theta {)}^2+{\left(a\sin \theta \right)}^2=a^2{\cos }^2\theta +a^2{\sin }^2\theta \\ =a^2({\cos }^2\theta +{\sin }^2\theta ) \\ Since, {\cos }^{2}a +{\sin }^{2}a=1 \\ Hence we get a^2\times 1=a^2=R.H.S. \\ Hence proved. \end{gathered}$$

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