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The chord P Q of the rectangular hyperbo...

The chord `P Q` of the rectangular hyperbola `x y=a^2` meets the axis of `x` at `A ; C` is the midpoint of `P Q ;` and `O` is the origin. Then ` A C O` is (a) equilateral (b) isosceles (c) right-angled (d) right isosceles

Text Solution

Verified by Experts

Hyperbola is
`xy=a^(2)`
`rArr" "2xy-2a^(2)=0`
Chord of PQ of hyperbola bisected at point C(h, k) is
`hy+kx-2a^(2)=2hk-2a^(2)`
`rArr" "(x)/(h)+(y)/(k)=2`
It meets x=axis at A (2h, 0).
Now, AC = OC = `sqrt(h^(2)+k^(2))`
Therefore, triangle OCA is isoscceles.
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