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Question

The length of the diameter of the circle x2+y2−4x−6y+4=0

A
9
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B
3
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C
4
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D
6
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Solution

The correct option is D 6

Consider the given circle equation.

x2+y24x6y+4=0 …… (1)

We know that the general equation of circle,

x2+y2+2gx+2fy+c=0 …… (2)

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

2g=4g=2

2f=6f=3

c=4

So, the centre of the circle

C=(g,f)

C=(2,3)

We know that the radius of circle,

r=g2+f2c

r=22+324

r=4+94

r=9=3

So, the diameter of this circle

d=2r=6

Hence, this is the answer.


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