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Find the equation of the circle passing through the point $(-1,-3)$ and having its centre at the point of intersection of the lines $x-2 y=4$ and $2 x+5 y+1$ $=0$.
The intersection of the lines: $x-2 y=4$ and $2 x+5 y+1=0$.
$\therefore$ This problem is same as solving a circle equation with centre and point on the circle given.
The general form of the equation of a circle is:
Where, (h, k) is the centre of the circle.
r is the radius of the circle.
In this question we know that $(h, k)=(2,-1)$, so for determining the equation of the circle we need to determine the radius of the circle.
Since the circle passes through $(-1,-3)$, that pair of values for $x$ and $y$ must satisfy the equation and we have:
⇒ Equation of circle is: