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Question

The shortest distance between the line y=x and the hyperbola x29y24=1 is

A
32 unit
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B
23 unit
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C
52 unit
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D
9 unit
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Solution

The correct option is C 52 unit
Any tangent to the hyperbola is
y=mx±9m24
for line y=x to have minimum distance from hyperbola tangent at the nearest point on the hyperbola should be parallel to given line
m=1
y=x±5
hence required distance
=501+1=52 unit

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