Given x ndash co ordinate of two points A and B are the roots of equation x sup2 2px q 0 and its y n...........

Quantitative Aptitude (CDS) Coordinate Geometry

Given x – co-ordinate of two points A and B are the roots of equation x²+2px+q=0 and its y – co-ordinate are roots of x²+2rx+s=0 find the equation of circle will AB has diameter.

x²+y²-2px-2ry-q-s=0

x²+y²+2px+2ry+q+s=0

x²+y²+4px+4ry+q+s=0

x²+y²-4px-4ry+q+s=0

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Explanation:

lets point A (x1 , y1) and B (x2 , y2)
x1 and x2 are root of equation x²+2px+q=0
y1 and y2 are roots of x²+2rx+s=0
here we find sum of roots product of roots
these points are as a diameter of the circle
hence equation of circle is given by
(x-x1)(x-x2) +(y-y1)(y-y2) = 0
Solving these we get x²+y²+2px+2ry+q+s=0