If anyone could check this answer for me, it would be greatly appreciated.

Find the equations relating the differentials on the curve $$9y^2= x^3 +3x^2$$ at the points $$(1,\frac{2}{3}), (-2,\frac{2}{3}), (-3,0)$$

Here's what I got:

$$y'= \frac {x^2+2x}{6y}$$

$$m @ (1,\frac{2}{3})= \frac {3}{4}$$
equation: 9x-12y-1=0

$$m @ (-2,\frac{2}{3})=0$$
equation: y= 2/3

$$m @ (-3,0)$$
does not exist

## Answers and Replies

xanthym
erik05 said:
If anyone could check this answer for me, it would be greatly appreciated.

Find the equations relating the differentials on the curve $$9y^2= x^3 +3x^2$$ at the points $$(1,\frac{2}{3}), (-2,\frac{2}{3}), (-3,0)$$

Here's what I got:

$$y'= \frac {x^2+2x}{6y}$$ <------ CORRECT

$$m @ (1,\frac{2}{3})= \frac {3}{4}$$
equation: 9x-12y-1=0 <----- CORRECT

$$m @ (-2,\frac{2}{3})=0$$
equation: y= 2/3 <----- CORRECT

$$m @ (-3,0)$$
does not exist <----- Should be the Vertical Line {x = -3}