Question

Find the centre and radius of the circle $2x^2+2y^2=3x-5y+7$

• A. $Centre:(\frac{3}{4},-\frac{5}{4})$; $Radius:\frac{3\sqrt{10}}{4}$
• B. $Centre:(-\frac{3}{4},\frac{5}{4})$; $Radius:\frac{3\sqrt{10}}{4}$
• C. $Centre:(\frac{3}{2},-\frac{5}{2})$; $Radius:\frac{3\sqrt{10}}{2}$
• D. None of these

Answer 1

The correct option is A $Centre:(\frac{3}{4},-\frac{5}{4})$; $Radius:\frac{3\sqrt{10}}{4}$

Given equation of circle is ${2x}^2+{2y}^2=3x-5y+7\Rightarrow {2x}^2+2y^2-3x+5y+7=0$
$\Rightarrow x^2+y^2-\frac{3}{2}x+\frac{5}{2}y+\frac{7}{2}=0$
Center $\equiv (-g,-f)=(\frac{3}{4},\frac{-5}{4})$
Radius $=\sqrt{g^2+f^2-c}=\sqrt{{\left(\frac{-3}{4}\right)}^2+{\left(\frac{5}{4}\right)}^2-\frac{7}{2}}=\frac{3\sqrt{10}}{4}$