circle

ellipse

focus

perihelion

$$x^2=16y$$

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$

$$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$

$$\frac{x}{b^2}+\frac{y}{a^2}=1$$

Major Axis

Minor Axis

Vertices

Co-Vertices

$$\frac{x^2}{4}+\frac{y^2}{16}=1$$  

$$\frac{x^2}{16}+\frac{y^2}{4}=1$$  

$$\frac{x^2}{16}+\frac{y^2}{64}=1$$  

$$\frac{x^2}{64}+\frac{y^2}{16}=1$$  

$$\frac{\left(x+1\right)^2}{4}+\frac{\left(y-2\right)^2}{9}=1$$

$$\frac{x^2}{25}+\frac{y^2}{9}=1$$

$$\left(x+1\right)^2+4\left(y-2\right)^2=16$$

$$\frac{\left(x-3\right)^2}{4}-\frac{\left(y+2\right)^2}{9}=1$$

a

2a

b

2b

$$\left(5,\ -4\right)\ and\ \left(5,\ 2\right)$$

$$\left(-2,\ -1\right)\ and\ \left(12,\ -1\right)$$  

$$\left(-1,\ -2\right)\ and\ \left(-1,\ 12\right)$$

$$\left(-4,\ 5\right)\ and\ \left(2,\ 5\right)$$

(0, 0)

(1, 5)

(1, 0)

(0, 1)

(0, 0)

(7, 1) and (-1, 1)

(3, -5) and (3, 7)

(3, 1)

(-8, 10); a = 12, b = 6

(-8, 10); a = 6, b = 12

(8, -10); a = 12, b = 6

(8, -10); a = 6, b = 12

$$\frac{\left(x-1\right)^2}{16}+\frac{\left(y+1\right)^2}{36}=1$$

$$\frac{\left(x-1\right)^2}{36}+\frac{\left(y+1\right)^2}{16}=1$$

$$\frac{\left(x+1\right)^2}{16}+\frac{\left(y-1\right)^2}{36}=1$$

$$\frac{\left(x+1\right)^2}{36}+\frac{\left(y-1\right)^2}{16}=1$$

$$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{25}=1$$

$$\frac{\left(x-3\right)^2}{25}+\frac{\left(y+2\right)^2}{9}=1$$

$$\frac{\left(x-3\right)^2}{9}+\frac{\left(y+2\right)^2}{25}=1$$

$$\frac{\left(x+3\right)^2}{25}+\frac{\left(y-2\right)^2}{9}=1$$

(4, 6)

( - 4, 3)

(6, 4)

(4, -3)

a = 10 , b = 6

a = 6 , b = 10

a = 36 , b = 100

a = 100 , b = 36

$$\frac{\left(x-5\right)^2}{36}+\frac{\left(y+5\right)^2}{11}=1$$  

$$\frac{x^2}{11}+\frac{y^2}{36}=1$$  

$$\frac{x^2}{36}+\frac{y^2}{11}=1$$  

$$\frac{\left(x+5\right)^2}{11}+\frac{\left(y-5\right)^2}{36}=1$$