Question

Let the abscissae of the two points P and Q on a circle be the roots of x2 – 4x – 6 = 0 and the ordinates of P and Q be the roots of y2 + 2y – 7 = 0. If PQ is a diameter of the circle x2 + y2 + 2ax + 2by + c = 0, then the value of (a + b – c) is

• A. 12
• B. 13
• C. 14
• D. 16

Answer 1

Answer: (A)

12

Answer 2

The correct answer is (A) : 12
Abscissae of PQ are roots of x2 – 4x – 6 = 0
Ordinates of PQ are roots of y2 + 2y – 7 = 0
and PQ is diameter
⇒ Equation of circle is $x^2+y^2−4x+2y−13=0$
But, given
$x^2+y^2+2ax+2by+c=0$
By comparison a = –2, b = 1, c = –13
⇒ a + b – c = –2 + 1 + 13 = 12