Question

A circle with center $(4,-5)$ is tangent to the $y$ -axis in the standard $(x,y)$ coordinate plane. What is the radius of this circle?

• (A) $4$
• (B) $5$
• (C) $\sqrt{41}$
• (D) $16$

Answer 1

The Correct Option is A

Explanation:
Equation of circle with center at $(h,k)$ and radius $r$ units is given by: $(x-h{)}^2+(y-k{)}^2=r^2$Here $(h,k)=(4,-5)$ and let the radius be $r$ units.The equation of the required circle is: $(x-4{)}^2+(y+5{)}^2=r^2$.$\because y$ -axis is the tangent to the circle $(x-4{)}^2+(y+5{)}^2=r^2$. So the co-ordinates of the point common to circle $(x-4{)}^2+(y+5{)}^2=r^2$ and the tangent $y$ -axis is $(0,-5)$.$\therefore$ The point $(0,-5)$ will satisfy the equation of circle.$\Rightarrow (0-4{)}^2+(-5+5{)}^2=r^2$$\Rightarrow r=4$So, the radius of the circle is $4$ units.Hence, the correct option is (A).