Question

The equation of any circle passing through the points of intersection of the circle $S = 0$ and the line $L = 0$ is

Answer 1

Hint: In this question, we are given that there is a circle which is passing through the points of intersection of the another circle whose equation is $S = 0$ and the line $L = 0$ and we have to find the equation of that circle. Here, we will use the condition that if the equation of the circle and line is equals to zero then there is a particular formula as the equation of the circle i.e., $S + \lambda L = 0$.

Formula used:
Equation of circle passing through the intersection point of a circle and a line –
$S + \lambda L = 0$

Complete step by step solution:
A circle is a closed curve drawn from a fixed point known as the centre, with all points on the curve being the same distance from the centre point.
Given that,
The equation of the circle is $S = 0$ and the equation of line is $L = 0$
Now, the circle is passing through the point of intersection of the circle $S = 0$ and line $L = 0$
Figure 1 is attached below,

Figure 1: Circles intersecting each other
The equation of the circle is $S + \lambda L = 0$
Here, $S$, $L$ are the equation of the circle and line.
Also, $\lambda $ is any variable.

Note: To solve such question, first try to make the figure and understand the question properly. This question is one of the type of family of circles. One of the most important topics in coordinate geometry is the family of circles. A family of circles is a large collection of circles. Circles with similar properties are combined in various ways to form the family of circles.