Question

Write the value of ‘C’ so that circle x2 + y2 +2gx + 2fy + c = 0 is concentric with the circle x2 + y2 + 6x + 8y + 5 = 0 and passing through point (1, 2).​

Answer 1

Step-by-step explanation:

Equation of circle is

x

2

+y

2

−8x−12y+15=0

On comparing that,

x

2

+y

2

+2gx+2fy+c=0

So,

(g,f)=(−4,−6)

(−g,−f)=(4,6)=(h,k)

Now, it passes through the point (5,4)

So,

Radius=

(4−5)

2

+(6−4)

2

Radius=

1+4

Radius=

5

So, equation of circle is,

(x−h)

2

+(y−k)

2

=r

2

⇒(x−4)

2

+(y−6)

2

=(

5

)

2

⇒x

2

+16−8x+y

2

+36−12y=25

⇒x

2

+y

2

−8x−12y+52=25

⇒x

2

+y

2

−8x−12y+27=0

Hence, this is the answer.