1. Writing Equations of Conics
From their graphs

2. Circles What is the center? (h, k) (-3, 3) What is the radius? r = 4
Plug these values into the formula
𝒙−𝒉 𝟐 + 𝒚−𝒌 𝟐 = 𝒓 𝟐
𝒙+𝟑 𝟐 + 𝒚−𝟑 𝟐 =𝟏𝟔

3. Ellipses What is the center? (h, k) (1, 5) What is the major axis?
What is the minor axis?
b= 4
Is it vertical or horizontal?
horizontal
Plug these values into the formula
𝒙−𝒉 𝟐 𝒂 𝟐 𝒚−𝒌 𝟐 𝒃 𝟐 =𝟏
𝒙−𝟏 𝟐 𝟔𝟒 𝒚−𝟓 𝟐 𝟏𝟔 =𝟏
Ellipses

4. Ellipses What is the center? (h, k) (-2, -4) What is the major axis?
What is the minor axis?
b= 3
Is it vertical or horizontal?
vertical
Plug these values into the formula
𝒚−𝒌 𝟐 𝒂 𝟐 𝒙−𝒉 𝟐 𝒃 𝟐 =𝟏
𝒚+𝟒 𝟐 𝟑𝟔 𝒙+𝟐 𝟐 𝟗 =𝟏
Ellipses

5. Hyperbolas What is the center? (h, k) (-5, 0)
What is the transverse axis?
a= 4
What is the conjugate axis?
b= 3
Is it vertical or horizontal?
vertical
Plug these values into the formula
𝒚−𝒌 𝟐 𝒂 𝟐 − 𝒙−𝒉 𝟐 𝒃 𝟐 =𝟏
𝒚+𝟓 𝟐 𝟏𝟔 − 𝒙 𝟐 𝟗 =𝟏
Hyperbolas

6. Hyperbolas What is the center? (h, k) (0, 0)
What is the transverse axis?
a= 2
What is the conjugate axis?
b= 4
Is it vertical or horizontal?
horizontal
Plug these values into the formula
𝒙−𝒉 𝟐 𝒂 𝟐 − 𝒚−𝒌 𝟐 𝒃 𝟐 =𝟏
𝒙 𝟐 𝟒 − 𝒚 𝟐 𝟏𝟔 =𝟏
Hyperbolas

7. Parabolas Is it vertical or horizontal? horizontal What is the vertex?
(h, k)
(2, 3)
What is the distance from the vertex to the focus?
P= 2
Use 𝒂= 𝟏 𝟒𝒑
𝒂= 𝟏 𝟒(𝟐) = 𝟏 𝟖
Plug these values into the formula
𝒙=𝒂 𝒚−𝒌 𝟐 +𝒉
𝒙= 𝟏 𝟖 𝒚−𝟑 𝟐 +𝟐
Parabolas

8. Parabolas Is it vertical or horizontal? vertical What is the vertex?
(h, k)
(3, -3)
What is the distance from the vertex to the focus?
P= 3
Use 𝒂= 𝟏 𝟒𝒑
𝒂= 𝟏 𝟒(𝟑) = 𝟏 𝟏𝟐
Plug these values into the formula
𝒚=𝒂 𝒙−𝒉 𝟐 +𝒌
𝒚= 𝟏 𝟏𝟐 𝒙−𝟑 𝟐 −𝟑
Parabolas