Question

A circle with center at $(3,2)$ and radius $5$ intersects the $x$-axis at a point whose $x$ co-ordinate is:

• A. $2.39$
• B. $4.58$
• C. $7.58$
• D. $8.00$
• E. $8.39$

Answer 1

The correct option is C $7.58$

The equation of circle is ${(x-3)}^2+{(y-2)}^2=25$
It will intersect $x$ -axis at $y=0$
Therefore ${(x-3)}^2=25-4=21$

$\Rightarrow x-3=\pm \sqrt{21}=\pm 4.5826$

$\Rightarrow x=7.58,-1.58$
The correct answer is option $C$.