Question

A circle passes through the points $(2,3)$ and $(4,5)$. If its centre lies on the line, $y-4x+3=0$, then its radius is equal to

• A. $\sqrt{5}$
• B. $1$
• C. $\sqrt{2}$
• D. $2$

Answer 1

Answer: (D)

$2$

Equation of the line through the given points is $y-3=x-2\Rightarrow x-y+1=0$.

Equation of the perpendicular line through the midpoint $(3,4)$ is $x+y-7=0$.

This intersects the given line at the center of the circle. So, the center of the circle is found to be $(2,5)$.

Clearly, the radius is then$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}=$ $\sqrt{(2-2{)}^2+(3-5{)}^2}=2$ units.

So the answer is option D.