The length of the latus rectum of the curve x | vedclass

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Question

(A) The given equation is $xy - 7x - 5y = 0$.Adding $35$ to both sides,we get $xy - 7x - 5y + 35 = 35$.This can be factored as $(x - 5)(y - 7) = 35$.T

Vedclass · Accepted Answer

$\sqrt{280}$

Vedclass · Answer

(A) The given equation is $xy - 7x - 5y = 0$.Adding $35$ to both sides,we get $xy - 7x - 5y + 35 = 35$.This can be factored as $(x - 5)(y - 7) = 35$.This represents a rectangular hyperbola of the form $(x - h)(y - k) = c^2$,where $c^2 = 35$.The length of the latus rectum of a rectangular hyperbola $(x - h)(y - k) = c^2$ is given by $2\sqrt{2c^2}$.Substituting $c^2 = 35$,we get $LR = 2\sqrt{2 	imes 35} = 2\sqrt{70} = \sqrt{4 	imes 70} = \sqrt{280}$.

The length of the latus rectum of the curve $xy = 7x + 5y$ is

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