The equation of the circle which intersects circles $x^{2} + y^{2} + x + 2 y + 3 = 0, x^{2} + y^{2} + 2 x + 4 y + 5 = 0$ and

$x^{2} + y^{2} - 7 x - 8 y - 9 = 0$ at right angle, will be

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Solution

The correct option is D

Let circle be $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ . Then according to the conditions given,

g + 2f = c + 3 .........(i)

2g + 4f = c + 5 .........(ii)

-7g - 8f = c - 9 ..........(iii)

$\Rightarrow g = \frac{2}{3}, f = \frac{2}{3}, c = - 1$

Therefore, the required equation is

$3 (x^{2} + y^{2}) + 4 (x + y) - 3 = 0.$

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The equation of the circle which intersects circles x2+y2+x+2y+3=0,x2+y2+2x+4y+5=0 and x2+y2−7x−8y−9=0 at right angle, will be

The correct option is D Let circle be x2+y2+2gx+2fy+c=0. Then according to the conditions given, g + 2f = c + 3 .........(i) 2g + 4f = c + 5 .........(ii) -7g - 8f = c - 9 ..........(iii) ⇒g=23,f=23,c=−1 Therefore, the required equation is 3(x2+y2)+4(x+y)−3=0.

The equation of the circle which intersects circles $x^{2} + y^{2} + x + 2 y + 3 = 0, x^{2} + y^{2} + 2 x + 4 y + 5 = 0$ and

$x^{2} + y^{2} - 7 x - 8 y - 9 = 0$ at right angle, will be