Find the slope of the tangent line to the curve at the

Question

1. Find the equation of the tangent line to the curve y = x² at x = 1.

This line is also tangent to a circle with center (18, 0) at x = 4. Find the equation of this circle.

2. Consider the curve defined by x² + y² - 3x + 13y = 13.

(a) Find dy/dx

(b) Under what condition on x is the tangent line to the curve horizontal?

(c) Under what condition on y is the tangent line to the curve vertical?

3. Consider the curve given by y = x/ (y + b).

(a) Find the slope of the tangent line to the curve at the point (0, 0). Your answer will have b in it.

(b) Find the equation of the tangent line to the curve at the point (0, 0). Your answer will have b in it.

4. You are given the circle, x² + y² = 25.

(a) At what two points is x = 4?

(b) Find the equation of the tangent line to the circle at Point A.

5. Find the slope of the tangent line to the curve at the point (-1, 2). Give an exact value.

x³ + 5x²y + 2y² = 4y +9.