The equation of the circle which touches x-axis at (0,0) and touc… - Vidyadip

MCQ

The equation of the circle which touches $x$-axis at $(0,0)$ and touches the line $3 x+4 y-5=0$ is:

A
$x^2+y^2-4 y=0$
B
$x^2+y^2-10 y=0$
C
$x^2+y^2+10 x=0$
✓
$x^2+y^2+10 y=0$

✓

Answer

Correct option: D.

$x^2+y^2+10 y=0$

$x^2+y^2+10 y=0$

Solution:
Equation of circle touching $x$-axis at $(0,0)$, means centre of circle lie on $Y$-axis i.e. $(0, k)$.
$(x-0)^2+(y-k)^2=k^2$
$S: x^2+y^2-2 k y=0$.... (1)
Circle S touches $3 x+4 y-5=0$
$\therefore \mathbf{k}=\frac{4 \mathbf{k}-5}{5}$
$5 k=4 k-5$
$k=-5$
$\therefore$ Equation of circle is
$\Rightarrow x^2+y^2+10 y=0$

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