Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems The circles whose equations are and will touch one another externally
MATHEMATICS · Single correct · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry
Problem The circles whose equations are x 2 + y 2 + c 2 = 2 a x x^2 + y^2 + c^2 = 2ax x 2 + y 2 + c 2 = 2 a x x 2 + y 2 + c 2 − 2 b y = 0 x^2 + y^2 + c^2 - 2by = 0 x 2 + y 2 + c 2 − 2 b y = 0 1 b 2 + 1 c 2 = 1 a 2 \frac{1}{b^2} + \frac{1}{c^2} = \frac{1}{a^2} b 2 1 + c 2 1 = a 2 1 1 c 2 + 1 a 2 = 1 b 2 \frac{1}{c^2} + \frac{1}{a^2} = \frac{1}{b^2} c 2 1 + a 2 1 = b 2 1 1 a 2 + 1 b 2 = 1 c 2 \frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2} a 2 1 + b 2 1 = c 2 1 1 b 2 + 1 c 2 = 2 a 2 \frac{1}{b^2} + \frac{1}{c^2} = \frac{2}{a^2} b 2 1 + c 2 1 = a 2 2 Browse the problem library