Question

Find the equation of the circle which is passing through the point (-2,-4) and concentric with the circle x² + y² - 12y - 23 = 0​

Answer 1

Step-by-step explanation:

Answer

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.