Question

Question #6fe41

Answer 1

`x=(2y)/a`

Explanation:

The slope of the implicit curve can be found first through differentiating the function with respect to `x`.

Recall that differentiating anything in terms of `y` will put the chain rule into effect, and that the product rule will be used to differentiate `axy`.

The derivative of the implicit function is

`d/dx(x^2-axy+y^2=a)=2x-ay-axdy/dx+2ydy/dx=0`

Solving for `dy/dx`, this becomes

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

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

Now, we must find when the tangent to the curve is parallel to the `y`-axis, which is when the slope, or `dy/dx`, is undefined.

`dy/dx=(ay-2x)/(2y-ax)` is undefined whenever its denominator, `2y-ax`, is equal to `0`.

Since lines parallel to the `y`-axis are in the form `x=?`, we can rearrange `2y-ax=0` to solve for `y`.

`2y-ax=0" "=>" "2y=ax" "=>" "x=(2y)/a`