Grade 11Analytical Geometry
equation of circle passing through (-1,-2) and concentric to the circle x2 +y2+3x+4y+1=0 is
equation of circle passing through (-1,-2) and concentric to the circle x2 +y2+3x+4y+1=0 is
2 Answers
Arun
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
(-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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