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Writing Equations of Conics
From their graphs
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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
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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
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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
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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
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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
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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
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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
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