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Find the limiting points of the circles and show that the square of the distance…
MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections
Problem Find the limiting points of the circles
( x 2 + y 2 + 2 g x + c ) + λ ( x 2 + y 2 + 2 f y + d ) = 0 (x^2 + y^2 + 2gx + c) + \lambda (x^2 + y^2 + 2fy + d) = 0 ( x 2 + y 2 + 2 g x + c ) + λ ( x 2 + y 2 + 2 f y + d ) = 0 and show that the square of the distance between them is
( c − d ) 2 − 4 f 2 g 2 + 4 c f 2 + 4 d g 2 f 2 + g 2 \frac{(c-d)^2 - 4f^2g^2 + 4cf^2 + 4dg^2}{f^2 + g^2} f 2 + g 2 ( c − d ) 2 − 4 f 2 g 2 + 4 c f 2 + 4 d g 2
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