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The number of possible tangents which ca...

The number of possible tangents which can be drawn to the curve `4x^2-9y^2=36 ,` which are perpendicular to the straight line `5x+2y-10=0` , is zero (b) 1 (c) 2 (d) 4

A

`5(y-3)=2(x-(sqrt(117))/(2)) `

B

` 2x-5y+10-2sqrt(18)=0 `

C

` 2x-5y-10-2sqrt(18)=0 `

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
` 4x^(2)-9y^(2)=36 rArr 8x-18y(dy)/(dx)=0 rArr (dy)/(dx)=(4x)/(9y) `
` therefore " Slope of the tangent " =(4x)/(9y) `
For this tangent to be perpendicular to the straight line ` 5x+2y-10=0, ` we must have
`(4x)/(9y)xx (-(5)/(2))=-1 rArr y=(10x)/(9). `
Putting this value of y in `4x^(2)-9y^(2)=36, ` we get `-64x^(2)=324, ` which does not have real roots. Hence, at no point on the given curve can the tangent be perpendicular to the given line.
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