Question

lf the circles $x^2+y^2-10x+2y+10=0$ and $x^2+y^2-4x-6y-12=0$ touch each other then the slope of the common tangent at the point of contact of the circles is

• A. $\frac{3}{4}$
• B. $\frac{4}{3}$
• C. $-\frac{4}{3}$
• D. $-\frac{3}{4}$

Answer 1

Answer: (A)

$\frac{3}{4}$

when two circles touch each other , thus equation of common tangent
is also a equation radical axis of those two given circle.
equation of radical axis is
$s_1-s_2=0$
$6x-8y-22=0$
$3x-4y-11=0$
So, $e{q}^n$ of tangent at point of contact is also
$3x-4y-11=0$
slope$=\frac{3}{4}.$