Question

If two circles. each of radius 5 units, touch each other at $(1,2)$ and the equation of their common tangent is $4x+3y=10$, then equation of the circle, a portion of which lies in all the quadrants is

• A. $x^2+y^2-10x-10y+25=0$
• B. $x^2+y^2+6x+2y-15=0$
• C. $x^2+y^2+2x+6y-15=0$
• D. $x^2+y^2+10x+10y+25=0$

Answer 1

Answer: (B)

$x^2+y^2+6x+2y-15=0$

Centre of the circle are given by
$\frac{x-1}{\cos \theta }=\frac{y-2}{\sin \theta }=5$
where $\tan \theta =\frac{3}{4},\cos \theta =\frac{4}{5},\sin \theta =\frac{3}{5}$ or $\cos \theta =\frac{-4}{5},\sin \theta =\frac{-3}{5}$
$\Rightarrow$ Centers are $(5,5)$ and $(-3,-1)$
and the circles are $x^2+y^2-10x-10y+25=0$ and $x^2+y^2+6x+2y-15=0$