Question

Equation having circle centre $(5,2)$ and which passes through the point $(1,-1)$ is

• A. $x^2+y^2-10x-4y-4=0$
• B. $x^2+y^2+10x+4y+4=0$
• C. $x^2+y^2-10x-4y-2=0$
• D. $x^2+y^2-10x-4y+4=0$

Answer 1

The correct option is A $x^2+y^2-10x-4y-4=0$

equation of circle,

$(x-h{)}^2+(y-k{)}^2=r^2$

$C=(5,2),P=(1,-1)$

$\Rightarrow (1-5{)}^2+(-1-2{)}^2=r^2$

$16+9=r^2$

$\therefore r=5$

Now,

$(x-5{)}^2+(y-2{)}^2=5^2$

$x^2+25-10x+y^2-4-4y=25$

$x^2+y^2-10x-4y-4=0$