The shortest distance between the line y=x and the hyperbola x29−y24=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±√9m2−4
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 =√5−0√1+1=√52 unit