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JEE Advanced Mathematics question

MathematicsHyperbolaJEE Advanced

Consider a branch of the hyperbola

- - 2Missing argument for \sqrt\sqrt2 x - 4Missing argument for \sqrt\sqrt2 y - 6 = 0

with vertex at the point . Let be one end of its latus rectum. If is the focus of the hyperbola nearest to the point then is

Answer: (B)

Solution

Complete squares: , i.e.

- = 1, X = x - Missing argument for \sqrt\sqrt2,\ Y = y + Missing argument for \sqrt\sqrt2.

So , , and , .

For the branch with vertex $A =

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Question ID VK-110670