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

Question

Let the abscissae of the two points P and Q on a circle be the roots of x2-4 x-6=0 and the ordinates of P and Q be the roots of y 2+2 y -7=0.If PQ is a diameter of the circle x2+y2+2 a x+2 b y+c=0, then the value of (a+b-c) is (A) 12 (B) 13 (C) 14 (D) 16

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/948bc36b69557259ad6fcaa44c70f8aa-.png" /> Equation of circle diameter form ( x - x 1)( x - x 2)+( y - y 1)( y - y 2)=0 (where x1, x2 are the roots of x2-4 x-6=0 and y1, y2 are the roots of y2+2 y-7=0 ) x2+y2-4 x+2 y-13=0 Now, Compare it with the given equation, we get a =-2, b =1, c =-13 Now a+b-c=12

Q. 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

12

13

14

16

Equation of circle diameter form (x−x1​)(x−x2​)+(y−y1​)(y−y2​)=0 (where x1​,x2​ are the roots of x2−4x−6=0 and y1​,y2​ are the roots of y2+2y−7=0 ) x2+y2−4x+2y−13=0 Now, Compare it with the given equation, we get a=−2,b=1,c=−13 Now a+b−c=12

Q. Let the abscissae of the two points $P$ and $Q$ on a circle be the roots of $x^{2} - 4 x - 6 = 0$ and the ordinates of $P$ and $Q$ be the roots of $y^{2} + 2 y - 7 = 0$ .If PQ is a diameter of the circle $x^{2} + y^{2} + 2 a x + 2 b y + c = 0$ , then the value of $(a + b - c)$ is