Question

The equation of the circle that touches the $Y$ - axis at a distance of $4$ units from the origin and cuts off an intercept of $6$ units on the $X$ - axis is

• A. $x^2+y^2\pm 5x-8y+16=0$
• B. $x^2+y^2\pm 2x-4y=0$
• C. $x^2+y^2\pm 3x-2y-8=0$
• D. $x^2+y^2\pm 10x-8y+16=0$

Answer 1

Answer: (D)

Equation of circle touches the $Y$ -axis at a distance 4 unit from origin

$(x-h{)}^2+(y-k{)}^2=r^2$
$O{A}^2=O{C}^2+A{C}^2$
$O{A}^2=4^2+3^2[AB=6]$
$O{A}^2=25=5^2$
$\therefore$ Equation of circle
$(x-h{)}^2+(y-4{)}^2=25$
Its also passes through $(0,4)$
$\because h^2=25\Rightarrow h=\pm 5$
$\therefore$ Equation of circle
$(x\pm 5{)}^2+(y-4{)}^2=25$
$x^2+y^2\pm 10x-8y+16=0$