Question

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

Options

• `2^2/7`

• `6/7`

• `7/6`

• `(-6)/7`

Answer 1

`6/7`

Explanation:

The curves is = `t^2 + 3t - 8, y = 2t^2 - 2t + 5`  ......(1)

Putting `x = 2, 2 = t^2 + 3t - 8`

∴ `t^2 + 3t - 10` = 0

or `(t + 5)(t - 2)` = 0

Putting `t = 2` in `y = 2t^2 - 2t - 5 = 8 - 4 - 5 = - 1`

At `x = 2, y = - 1, t = 2`

Differentiating (1)

`(dx)/(dt) = 2t + 3, (dy)/(dt) = 4t - 2`

`(dy)/(dx) = (dy)/(dt) + (dx)/(dt) = (4t - 2)/(2t + 3)`

At `(t = 2) (dy)/(dx) = (4 xx 2 - 2)/(2 xx 2 + 3) = 6/7`