Equation $x = 5 + 3 Cos\alpha$ and $y = 7 + 3Sin\alpha$ is combinally a—

Explanation

$x = 5 + 3 Cos\alpha$ $y = 7 + 3 Sin\alpha$ $Cos\alpha = \frac{x-5}{3}$ $Sin\alpha = \frac{y-7}{3}$ On squaring both sides- $Cos^2\alpha = \left(\frac{x-5}{3}\right)^2, Sin^2\alpha = \left(\frac{y-7}{3}\right)^2$ $\Rightarrow \because Sin^2\alpha + Cos^2\alpha = 1$ $\Rightarrow \therefore \left(\frac{x-5}{3}\right)^2 + \left(\frac{y-7}{3}\right)^2 = 1$ $\Rightarrow (x-5)^2 + (y-7)^2 = 3^2$ $\Rightarrow$ It is an equation of circle whose radius is 3 and centre is (5,7). Note—$x^2 + y^2 = a^2$ is an equation of circle