Question

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

Answer 1

Answer:

The diameter of the circle is 6 units.

Step-by-step explanation:

The given equation of circle is-

$x^{2} +y^{2} -4x - 6y + 4 = 0$

Compare this with general equation-

$x^{2} +y^{2}+2gx+2fy+c = 0$

Here 2g = -4, 2f = -6 and c = 4

g = -2, f =  -3 and c = 4

We know that-

$Radius \ of \ a \ circle \ = \sqrt{g^{2}+f^{2}-c }$

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

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

$r = \sqrt{9}$

r = 3 units

Radius = 3 units

We know that-

Diameter = 2r

D = 2×3

D = 6 units

Hence, the diameter of the circle is 6 units.

Answer 2

Answer:

Correct option is D)

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⇒g=−2

2f=−6⇒f=−3

c=4

So, the centre of the circle

C=(−g,−f)

C=(2,3)

We know that the radius of circle,

r=

g

2

+f

2

−c

​

r= 22+32 −4

​

r= √4+√9−√4

​r= √9 =3

So, the diameter of this circle

d=2r=6

Hence, this is the answer.