Question

If two diameters of a circle lie along the lines $x-y=9$ and $x-2y=7,$ and the area of the circle is 38.5 sq cm, find the equation of the circle.

Answer 1

We kinow that the point of intersection of two diameters of a circle is the centre of the circle.

On solving $x-y=9$ and $x-2y=7,$ we get the centre as $C(11,2).$

Now, $\pi r^2=\frac{77}{2}\iff |r^2|=(\frac{77}{2}\times \frac{7}{22})=\frac{49}{4}\iff r=\frac{7}{2}.$

$\therefore$ the required equation is $(x-11{)}^2+(y-2{)}^2=\frac{49}{4}.$