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The smallest possible positive slope of ...

The smallest possible positive slope of a line whose y-intercept is 5 and which has a common point with the ellipse `9x^(2)+16y^(2)=144` is-

A

`3/4`

B

`1`

C

`4/3`

D

`9/16`

Text Solution

Verified by Experts

The correct Answer is:
B
ellipse `x^(2)/16+y^(2)/9=1`
Any tengent `(x cos theta)/(4)+(y sin theta)/3=1`
y intercept `=5 rArr sin theta =3/5 , theta in (pi/2, pi)`
`rArr cos theta =-4/5`
tangent `rArr - x/5+y/5=1rArr" slope"=1`
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