The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 7 - Systems of Circles>EXAMPLES XXIV>Q 13

HARD

JEE Advanced

IMPORTANT

Earn 100

The equation of the circle which is orthogonally cutting the three circles $x^{2} + y^{2} = a^{2}, {(x - c)}^{2} + y^{2} = a^{2}$ and $x^{2} + {(y - b)}^{2} = a^{2}$ (where $a, b, c \neq 0$ ) is $p x^{2} + p y^{2} - c x - b y + a^{2} = q$ . Find $2 (p + q + 2)$ .

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Important Questions on Systems of Circles

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 7 - Systems of Circles>EXAMPLES XXIV>Q 14

The equation of the circle which is orthogonally cutting the three circles

x^{2} + y^{2} - 2 x + 3 y - 7 = 0, x^{2} + y^{2} + 5 x - 5 y + 9 = 0

and

x^{2} + y^{2} + 7 x - 9 y + 29 = 0

is

x^{2} + y^{2} - a x + b y - c = 0

. Find

a + b + c

.

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 7 - Systems of Circles>EXAMPLES XXIV>Q 15

Show that the equation of the circle which is cutting orthogonally the circles

{(x - a)}^{2} + {(y - b)}^{2} = b^{2}, {(x - b)}^{2} + {(y - a)}^{2} = a^{2}

and

{(x - a - b - c)}^{2} + y^{2} = a b + c^{2}

is

x^{2} + y^{2} - 2 x (a + b) - y (a + b) + a^{2} + 3 a b + b^{2} = 0

. (where

a \neq b

)