Question

$f(x,y)=x^2+y^2+2ax+2by+c=0$ represents a circle. If $f(x,0)=0$ has equal roots, each being $2$ and $f(0,y)=0$ has $2$ and $3$ as it's roots, then centre of circle is

• A. $(2,\frac{5}{2})$
• B. Data are not sufficient
• C. $(-2,-\frac{5}{2})$
• D. Data are inconsistent

Answer 1

The correct option is D Data are inconsistent

$x^2+2ax+c=(x-2{)}^2$
$\Rightarrow$ $-2a=4,c=4$
$\Rightarrow$ $a=-2,c=4$
$y^2+2by+c=(y-2)(y-3)$
$\Rightarrow$ $-2b=5,c=6$
$\Rightarrow$ $b=-\frac{5}{2},c=6$ clearly the data are not consistent.