the equation of the circle concentric with x^2+y^2-2x+8y-23=0 and passing through (2,3) is
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Find the equation of the circle concentric with the circle x
2
+y
2
−8x−12y+15=0 and passing through the point (5, 4).
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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
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