Question

The length of the diameter of the circle $x^2+y^2-4x-6y+4=0$

• A. $9$
• B. $3$
• C. $4$
• D. $6$

Answer 1

The correct option is D $6$

Consider the given circle equation.

$x^2+y^2-4x-6y+4=0$ …… (1)

We know that the general equation of circle,

$x^2+y^2+2gx+2fy+c=0$ …… (2)

On comparing equation (1) and (2), we get

$2g=-4\Rightarrow g=-2$

$2f=-6\Rightarrow f=-3$

$c=4$

So, the centre of the circle

$C=(-g,-f)$

$C=(2,3)$

We know that the radius of circle,

$r=\sqrt{g^2+f^2-c}$

$r=\sqrt{2^2+3^2-4}$

$r=\sqrt{4+9-4}$

$r=\sqrt{9}=3$

So, the diameter of this circle

$d=2r=6$

Hence, this is the answer.