## Question

A, B, C and D are the points of intersection of a circle and a rectangular hyperbola which have different centers. If AB passes through the center of the hyperbola, then CD passes through

### Solution

Center of circle

If the centers of the circle and hyperbola are and (h, k) and the points are A(*x*_{1}, *y*_{1}), B(*x*_{2}, *y*_{2}), C(*x*_{3}, *y*_{3}) and D(*x*_{4}, *y*_{4}), then

….. (1)

(h, k) lies on AB, then chords of the hyperbola, passing through its center, are bisected at the center, so and hence

is the mid-point of CD and lies on CD.

#### SIMILAR QUESTIONS

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