Equations for Parabola, Hyperbola, and Ellipse

Vocabulary and formula flashcards for conic sections including parabola, hyperbola, and ellipse equations, vertices, and foci coordinates as referenced in the lecture transcript.

Vertical Parabola Standard Equation

$(x-h) = 4p(y-k)$ where $p=0$

Vertical Parabola Focus

$$(h, k+p)$$

Vertical Parabola Directrix

$$y = k-p$$

Vertical Parabola Axis

$$x = h$$

Horizontal Parabola Standard Equation

$(y-k) = 4p(x-h)$ where $pzo$

Horizontal Parabola Focus

$$(h, k-p)$$

Horizontal Parabola Directrix

$$x = h-p$$

Horizontal Parabola Axis

$$y = k$$

Vertical Hyperbola Standard Equation

$$\frac{(y-k)^2}{ac} - \frac{(x-h)^2}{b3} = 1$$

Vertical Hyperbola Vertices

$(h, kta)$ and $(h, k-a)$

Vertical Hyperbola Conjugate Axis

$(h+b, k)$ and $(h-b, k)$

Vertical Hyperbola Foci

$(h, k+c)$ and $(h, k-c)$

Horizontal Hyperbola Foci

$$(h, ktb)$$

Hyperbola Distance Formula (c)

$$c = \sqrt{a^2+b^2}$$

Vertical Ellipse Standard Equation

$$\frac{(x-h)^2}{62} + \frac{(y-k)^2}{az} = 1$$

Vertical Ellipse Vertices

$(h, kta)$ and $(h, k-a)$

Vertical Ellipse Co-vertices

$(h+b, k)$ and $(h-b, k)$

Vertical Ellipse Foci

$(h, ktc)$ and $(h, k-c)$

Horizontal Ellipse Vertices

$(h+a, k)$ and $(h-a, k)$

Horizontal Ellipse Co-vertices

$(h+b, k)$ and $(h-b, k)$

Horizontal Ellipse Foci

$(h+c, k)$ and $(h-c, k)$

Ellipse Distance Formula (c)

$$c = \sqrt{a^2b^2}$$