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Distance between the parallel tangents h...

Distance between the parallel tangents having slope `-(4)/(3)` to the ellipse `(x^(2))/(18)+(y^(2))/(32) = 1` , is

A

`24`

B

`(24)/(5)`

C

`(48)/(5)`

D

`(96)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
Distance between ………….

`y = mx +- sqrt(a^(2)m^(2)+b^(2))`
`y = -(4)/(3)x +- sqrt(18xx(16)/(9)+32)`
`y= - (4)/(3)x +- 8`
Distance between tangents `= (16)/(sqrt(1+(16)/(9))) = (16xx3)/(5) = (48)/(5)`
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