Question

The circle ${\mathrm{x}}^2+{\mathrm{y}}^2+6\mathrm{y}=0$ touches

• A. y-axis at the origin
• B. x-axis at the origin
• C. x-axis at the point $\left(3,0\right)$
• D. the line $y+3=0$

Answer 1

The correct option is B

x-axis at the origin

Explanation for the correct option:

Given,

the circle equation: ${\mathrm{x}}^2+{\mathrm{y}}^2+6\mathrm{y}=0$

[Adding and subtracting the $3^2$]

$\Rightarrow {\mathrm{x}}^2+{\mathrm{y}}^2+6\mathrm{y}+3^2-3^2=0$

$\Rightarrow x^2+{(y+3)}^2=9$

So, Radius $=3$

center $=\left(0,3\right)$

So, it touches x-axis at the origin.

Hence, the correct option is (B)