Question

Find the equation of the circle which touches the y-axis at a distance of 4 units from the origin and cuts an intercept of 6 units from the axis of x.

Answer 1

Consider the diagram shown below.

The circle touches y-axis at $(0,4)$. SO, the centre will lie on $y=4$. Therefore, y-coordinate of the circle will be $4$.

Now,

$CD=6$

$\Rightarrow CM=3$

Again,

$RM=4$

Using Pythagoras theorem, we have

$CR=\sqrt{3^2+4^2}=5$ $=$ Radius of the circle

Therefore,

Centre of the circle, $R=(5,4)$

Therefore, required equation of the circle is,

${(x-5)}^2+{(y-4)}^2=5^2$

$x^2+y^2-10x-8y+16=0$

Hence, this is the required result.