Question

A circle of radius $5$ units passes through the points $(7,1),(9,5)$. If the ordinate of the centre is less than $2$, then the equation of the circle is

• A. $x^2+y^2+8x-10y+16=0$
• B. $x^2+y^2+8x+10y+16=0$
• C. $x^2+y^2-24x-2y+120=0$
• D. $x^2+y^2+24x-2y-120=0$

Answer 1

Answer: (C)

$x^2+y^2-24x-2y+120=0$

Let $(h,k)$ is a centre of circle , so

$(h-7{)}^2+(k-1{)}^2=25$
and $(h-9{)}^2+(k-5{)}^2=25$

$Let{x}^2+y^2+2gx+2fy+c=0$ is circle .
so, $(7,1)$ lies on circle so,

$50+14g+2f+c=0$ ----(1)
$(9,5)$ lies on circle

$106+18g+10f+c=0$ ----(2)

and $g^2+f^2-c=25$ -----(3)
From (1) & (2),
$4g+8f+56=0$

$g+2f+14=0$
From (1), (2), (3), (4),
$g=-12$ and $f=-1,c=120$

so, $e{q}^n$ of circle is

$x^2+y^2-24x-2y+120=0$