Question

A circle touches positive $x-$axis at a distance of $9$ units from the origin and makes an intercept of $24$ units on negative direction of $y-$axis. Then

• A. Radius of circle is $15$ units.
• B. Equation of circle is $(x-9{)}^2+(y+15{)}^2={15}^2$.
• C. Radius of circle is $13$ units.
• D. Equation of circle is $(x-9{)}^2+(y+13{)}^2={13}^2$.

Answer 1

Answer: (A), (B)

The correct options are
A Radius of circle is $15$ units.
B Equation of circle is $(x-9{)}^2+(y+15{)}^2={15}^2$.

Centre of the circle : $C\equiv (9,h)$ and the circle cuts the $y-$axis at points $A$ and $B$ and mid point of $AB$ is $M$.
In $△AMC,$
$AC=r=|h|$
$\Rightarrow A{C}^2=A{M}^2+M{C}^2$
$\Rightarrow r^2={12}^2+9^2=225=h^2$
For intercept on negative direction of $y-$axis,
$r=15,h=-15$
$\therefore$ Equation of circle with centre $(9,-15)$ is $(x-9{)}^2+(y+15{)}^2=225$