Question

The range of values of 'a' for which the points (a, 4) is outside the two circles $x^2+y^2+10x=0$ and $x^2+y^2-12x+20=0$ is

• A. $(-\infty ,-8)$
• B. $(-\infty ,-8)\cup (-2,6)\cup (6,\infty )$
• C. $(-8,-2)$
• D. none of these

Answer 1

The correct option is B $(-\infty ,-8)\cup (-2,6)\cup (6,\infty )$

Given that$(a,4)$lies outside the circles so
$x^2+y^2+10x=0$
$x^2+y^2+12x+20=0$
$a^2+10a+16>0$
$a^2+12a+36>0$
by solving the equations we get
$aϵ(-\alpha ,-8)\cup (-2,\alpha )$