Question

The radius of the tangent circle that can be drawn to pass through the points $(0,7)$ and $(0,6)$ and touching the $x$-axis is

• A. $5/2$
• B. $3/2$
• C. $7/2$
• D. $9/2$

Answer 1

Answer: (C)

The equation of any circle through $(0,1)$ and $(0,6)$ is
$x^2+(y-1)(y-6)+\lambda x=0$
or $x^2+y^2+\lambda x-7y+6=0$
If it touches the $x$-axis, then $x^2+\lambda x+6=0$
should have equal roots, i.e.,
${\lambda }^2=24$ or $\lambda =\pm \sqrt{24}$
Radius of these circles $=\sqrt{6+\frac{49}{4}-6}$
$=\frac{7}{2}$ units
So, we can draw two circles but the radius of each circle is $7/2$.