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The abscissa of 2 points A,B are the roots of equation x^2+2x-a^2=0 and ordinate are roots of equation y^2+4y-b^2=0 .Find equation of circle with AB diameter??

The abscissa of 2 points A,B are the roots of equation x^2+2x-a^2=0 and ordinate are roots of equation y^2+4y-b^2=0 .Find equation of circle with AB diameter??

Grade:11

1 Answers

Ritesh Khatri
76 Points
4 years ago
Let A(x1,y1) and B(x2,y2)
Eqn of circle is (x – x1)(x – x2) + (y – y1)(y – y2) = 0
x2 – (x1 + x2)x +x1x2 + y2 – (y1 + y2)y +y1y2 = 0
x2 – (-2)x + (-a2)+ y2 – (-4)y +(-b2) = 0
x2 + 2x – a2+ y2 + 4y – b2 = 0
x2 + y+ 2x + 4y – a2  – b2 = 0
is required eqn

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