Chapter 10

Question 1

A parabola with a vertical axis

• standard form?
• equation to find the directrix?
• focus point?
• other points if p > 0?
• other points if p < 0?

Answer 1

• (x - h)^2 = 4p(y - k)
• y = k - p
• (h, k + p)
• (h - 2p, k + p), (h + 2p, k + p)
• (h - |2p|, k + p), (h + |2p|, k + p)

Question 2

A parabola with a horizontal axis

• standard form?
• equation to find the directrix?
• focus point?
• other points if p > 0?
• other points if p < 0?

Answer 2

• (y - k)^2 = 4p(x - h)
• x = h - p
• (h + p, k)
• (h + p, k + 2p), (h + p, k - 2p)
• (h + p, k + |2p|), (h + p, k - |2p|)

Question 3

An ellipse whose major axis is horizontal

• standard form?
• foci?
• vertices?
• co-vertices?

Answer 3

• (x - h)^(2)/a^2 + (y - k)^(2)/b^2 = 1 *a > b
• (h ± c, k) *c^2 = a^2 - b^2
• (h ± a, k)
• (h, k ± b)

Question 4

An ellipse whose major axis is vertical

• standard form?
• foci?
• vertices?
• co-vertices?

Answer 4

• (x - h)^(2)/b^2 + (y - k)^(2)/a^2 = 1 *a > b
• (h, k ± c) *c^2 = a^2 - b^2
• (h, k ± a)
• (h ± b, k)

Question 5

A hyperbola whose transverse axis is horizontal

• standard form?
• vertices?
• co-vertices?
• foci?

Answer 5

• (x - h)^(2)/a^2 - (y - k)^(2)/b^2 = 1
• (h ± a, k)
• (h, k ± b)
• (h ± c, k) *c^2 = a^2 + b^2

Question 6

A hyperbola whose transverse axis is vertical

• standard form?
• vertices?
• co-vertices?
• foci?

Answer 6

• (y - k)^(2)/a^2 - (x - h)^(2)/b^2 = 1
• (h, k ± a)
• (h ± b, k)
• (h, k ± c) *c^2 = a^2 + b^2

Question 7

Eccentricity of an Ellipse

Answer 7

e = c/a

Question 8

dy/dx = ?

Answer 8

(dy/dt)/(dx/dt) *t and θ both work in this formula

Question 9

d^(2)y/dx^(2) = ?

Answer 9

d/dt[dy/dx]/(dx/dt) *t and θ both work in this formula

Question 10

Arc length

Answer 10

integral from “a” to “b”: [square root of: (dx/dt)^2 + (dy/dt)^2) * dt]

Question 11

Polar Arc length

Answer 11

integral from “α” to “β”: [square root of: r^2 + (dr/dθ)^2) * dθ]

Question 12

Polar Area

Answer 12

(1/2) * integral from “α” to “β”: [(r(θ))^2 * dθ]