If the abcissiae and ordinates of two points P and Q are the roots of equations x2 + 2ax - b2 = 0 and y2 + 2py - q2 = 0 respectively, then the equation of the circle with PQ as diameter is

Question

If the abcissiae and ordinates of two points P and Q are the roots of equations x2 + 2ax - b2 = 0 and y2 + 2py - q2 = 0 respectively, then the equation of the circle with PQ as diameter is (A) x2 + y2 + 2ax + 2py - b2 - q2 = 0 (B) x2 + y2 - 2ax - 2py + b2 + q2 = 0 (C) x2 + y2 - 2ax - 2py - b2 - q2 = 0 (D) x2 + y2 + 2ax + 2py + b2 + q2 = 0

Tardigrade Admin · Accepted Answer

Correct answer is (a) x2 + y2 + 2ax + 2py - b2 - q2 = 0

Q. If the abcissiae and ordinates of two points P and Q are the roots of equations $x^{2} + 2 a x - b^{2}$ = 0 and $y^{2} + 2 p y - q^{2}$ = 0 respectively, then the equation of the circle with PQ as diameter is

$x^{2} + y^{2} + 2 a x + 2 p y - b^{2} - q^{2} = 0$

$x^{2} + y^{2} - 2 a x - 2 p y + b^{2} + q^{2} = 0$

$x^{2} + y^{2} - 2 a x - 2 p y - b^{2} - q^{2} = 0$

$x^{2} + y^{2} + 2 a x + 2 p y + b^{2} + q^{2} = 0$

Correct answer is (a) $x^{2} + y^{2} + 2 a x + 2 p y - b^{2} - q^{2} = 0$

Q. If the abcissiae and ordinates of two points P and Q are the roots of equations x2+2ax−b2 = 0 and y2+2py−q2 = 0 respectively, then the equation of the circle with PQ as diameter is

x2+y2+2ax+2py−b2−q2=0

x2+y2−2ax−2py+b2+q2=0

x2+y2−2ax−2py−b2−q2=0

x2+y2+2ax+2py+b2+q2=0