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Question

Column 1 has the condition on circle and column 2 has the equation of circles.which one of them are matched correct?

Column 1 column 2

1) Centre of origin and radius = 10 P) (x8)(x+8)+(y6)(y+6)=0

2) Extremeties of diameter are (8,6) and (-8,-6) Q) (x6)(x+6)+(y8)(y+8)=0

3) Centre is (1,-2) and radius is 4 R) x2 + y2 2x + 4y 11 = 0

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Solution

1) Equation of circle with origin as centre and radius r is given by x2 + y2 = r2
x2 + y2 = 100 is the equation of the circle we will expand the equation given P and check if it gives same equation x2 + y2 = 100 .
(x8)(x+8) + (y6)y+6=0
x2 64 + y2 36 = 0
x2 + y2 = 100
So both of them give the same equation

2) Equation of circle with (x1,y1) and (x2,y2) as the extremeties of diameter is given by
(xx1)(x,x2) + (yy1)(yy2)
(x8) (x+8)+(y6) (y+6)=0
(x2 + y2 = 100
We will expand Q and see it gives the same equation.
(x6)(x+6)+(y8)(y+8)=0
x2 + y2 = 100
2 is correctly matched

3) Equation of a circle with centre (h,k) and radius r is given by
(xh)2 + (yk)2 = r2
(x1)2 + (y+2)2 = 42
x2 + y2 2x + 4y + 1 + 4 =16
x2 + y2 2x + 4y 11 = 0

3 is correctly matched.


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