Question

If the circles $x^2+y^2-9=0$ and $x^2+y^2+2ax+2y+1=0$ touch each other, then $a=$

• A. -4/3
• B. 0
• C. 1
• D. 4/3

Answer 1

Answer: (A), (D)

4/3
-4/3

When two circle touch each other externally, then

$r_1+r_2=\sqrt{{\{0-(-a\left)\right\}}^2+{\{0-(-1\left)\right\}}^2}$

$\Rightarrow 3+a=\sqrt{a^2+1}$

$\Rightarrow a=-\frac{4}{3}$

When two circle touch each other internally, then

$|r_1-r_2|=\sqrt{{\{0-(-a\left)\right\}}^2+{\{0-(-1\left)\right\}}^2}$

$\Rightarrow |3+a|=\sqrt{a^2+1}$

$\Rightarrow a=\frac{4}{3}$