A tilted oval: tangent lines and a moving point

The question

Name: ______________________   Date: ____________   A tilted oval: tangent lines and a moving point (9 points)

1. (a) Show that $\frac{dy}{dx}$$= \frac{y - 2x - 2}{2y - x - 1}$. [2 points]

2. (b) Write an equation for the line tangent to the curve at the point $(0, -1)$. [1 point]

3. (c) Find the coordinates of all points on the curve at which the line tangent to the curve is horizontal. [3 points]

4. (d) A particle moves along the curve. At the instant the particle passes through the point $(1, 1)$, $\frac{dy}{dt} = 3$. Find $\frac{dx}{dt}$ at that instant. Explain what your answer shows about the tangent line at $(1, 1)$. [3 points]