The value of λ for which the circle x2+y2-3x+λy-5=0 and 4(x2+y2)-12x-y-9=0becomes concentric is
The value of λ for which the circle x2+y2-3x+λy-5=0 and 4(x2+y2)-12x-y-9=0becomes concentric is
Ateeq khan , 5 Years ago
Grade 12th pass
Analytical Geometry> The value of λ for which the circle x 2...
1 Answers
Ram Kushwah
Last Activity: 4 Years ago
GIVEN:
EQUATION OF TWO CIRCLES AS:
x²+y²-3x+λy-5=0.......................(1)
and 4(x²+y²)-12x-y-9=0
Or x²+y²-3x-y/4-9/4=0...................(2)
TO FIND:
Value of λ If circle (1) and (2) become concentric
SOLUTION:
The std equation of a circle is:
x²+y²+2gx+2fy+c=0...................(3)
centre is (-g,-f)
comparing (2) and (3) we get
g=-3/2 ,f=-1/8,c=-9/4
So centre of circle (2) is (-3/2,-1/8)
Now comparing (1) and (3) we get
g=-3/2,f=λ/2
So centre of circle (1) is (-3/2,λ/2)
Circle(1) and (2) become concentric if the centre of both the
circles is same
Thus the centre of circle (1) is (-3/2,-1/8)
On comparision we get
x coordinates are same
and y coordinate
λ/2=-1/8
λ=-2/8=-1/4
RESULT:
λ = -1/4
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