Question

Find the slope of tangent line at (1,-1.5)

Answer 1

The slope of the tangent m = -0.0833

Explanation:

Step(i):-

Given that the curve

x y - 2y² + x² = -5 ...(i)

Differentiating equation (i) with respective to 'x', we get

`x((dy)/(dx) )+y (1) -2(2y)(dy)/(dx) + 2x=0`

`x((dy)/(dx) ) -2(2y)(dy)/(dx) = -2x-y`

`(x -4y)(dy)/(dx) = -2x-y`

`(dy)/(dx) = (-2x-y)/(x-4y)`

Step(ii):-

The slope of the tangent

`((dy)/(dx))_(1,-1.5) = (-2x-y)/(x-4y)`

`((dy)/(dx))_(1,-1.5) = (-2(1)-(-1.5))/(1-4(-1.5))`

m =
`(-2+1.5)/(1+6)`

`m = (-0.5)/(6) = -0.083`

The slope of the tangent m = -0.0833