Question

The equation of circle of radius $\sqrt{17}$ unit, with centre on the positive side of $x$-axis and through the point $(0,1)$ is

• A. $x^2+y^2-8x-1=0$
• B. $x^2+y^2+8x-1=0$
• C. $x^2+y^2-9y+1=0$
• D. $2x^2+2y^2-3x+2y=4$

Answer 1

The correct option is A $x^2+y^2-8x-1=0$

Radius = $\sqrt{17}$
Centre on positive side of x-axis i.e., ($\alpha ,0$)

$\therefore$ Equation of circle in $(x-\alpha {)}^2+y^2=(\sqrt{17}{)}^2$

Since, it passes through $(0,1)$
$\therefore {\alpha }^2+1^2=17\Rightarrow {\alpha }^2=16\Rightarrow \alpha =4$

$\therefore$ Equation of circle is,
$(x-4{)}^2+y^2=17\Rightarrow x^2+y^2-8x-1=0$