Circles are drawn on chords of rectangular hyperbola xy = c^2 parallel to line y = x as diame

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10-2. Parabola, Ellipse, Hyperbola

normal

Circles are drawn on chords of the rectangular hyperbola $ xy = c^2$ parallel to the line $ y = x $ as diameters. All such circles pass through two fixed points whose co-ordinates are :

$(c, c)$

$(- c, - c)$

$(- c, c)$

both $(A)$ and $(B)$

Solution

$1/(t_1t_2) = – 1; $ $(x – ct_1) (x -ct_2) $+$\left( {y\,\, – \,\,{\textstyle{c \over {{t_1}}}}} \right)$$\left( {y\,\, – \,\,{\textstyle{c \over {{t_2}}}}} \right)$ $ = 1$
use $t_1t_2 = – 1 $ gives
$(x^2 + y^2 – 2c^2) – (t_1 + t_2) (x – y) = 0 $ $\Rightarrow $ $S + \lambda L = 0 $

Standard 11

Mathematics

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If the circle $x^2 + y^2 = a^2$ intersects the hyperbola $xy = c^2 $ in four points $ P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3), S(x_4, y_4), $ then

normal

Circles are drawn on chords of the rectangular hyperbola $ xy = c^2$ parallel to the line $ y = x $ as diameters. All such circles pass through two fixed points whose co-ordinates are :

Solution

Similar Questions

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