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equation of circle passing through (-1,-2) and concentric to the circle x 2 +y 2 +3x+4y+1=0 is

equation of circle passing through (-1,-2) and concentric to the circle x2 +y2+3x+4y+1=0 is

Grade:11

2 Answers

Arun
25757 Points
4 years ago
Dear student
 
concemtric circle means it is with same centre.
hence centre of required circle = (-3/2, -4/2)
 
also it passes throgh (-1, -2)
hence radius= sqrt (1/4) = ½
 
hence equation of circle
 (x+3/2)^2 + (y+2)^2= 1/4
 
Navaneeth
13 Points
one year ago
(-1,-2).  X^2+Y^2-3x+4Y-c=0
X^2+Y^2-3X+4Y-C=0
2G=3.         2F=4.    (from ax^2+by^2+2hxy+2gx+2fy+c=0 
   G=-3/2.      F=2.        In which 2hxy=0 and c=0)
-G=3/2.         -F=-2
therefore (-3/2,--2)
R=√(-3/2+2)^2+(0)^2   [ (x-h)^2+(y-k)^2=r^2 ]
R=√(5/2)^2
R=√25/4=5/2
(r-h)^2+(y-k)^2=r^2
(x-3/2)^2+(y+2)^2=25/4
x^2-3x+9/4+y^2+4y+4=25/4
x^2+y^2-3x+4y+9/4+4=25/4
X^2+y^2-3x+4y+25/4=25/4
x^2+y^2-3x+4y=0 is the equation of the circle 
 
 

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