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The slope of the tangent to the curve x=...

The slope of the tangent to the curve `x=t^2+3t-8,``y=2t^2-2t-5`at the point `(2, -1)`is

A

`7//6`

B

`6//7`

C

1

D

`5//6`

Text Solution

Verified by Experts

The correct Answer is:
B
`(dx)/(dt)=2t+3,(dy)/(dt)=4t-2`
`(dy)/(dx)=(dy//dt)/(dx//dt)=(4t-2)/(2t+3)`
Slope at `t =2 =(dy)/(dx)//t=2=(4(2)-2)/(2(2)+3)=6/7`
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