Hyperbola Pre-Calculus PDF
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This document serves as notes on hyperbola equations. It includes different cases related to hyperbola equations and examples.
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Hyperbola PRE-CALCULUS WEEK 6: 1ST QUARTER LEARNING OBJECTIVES: Define a hyperbola Transform standard equations of hyperbola into general form and vice versa Graph hyperbolas HYPERBOLA The definition of a hyperbola is similar to that of an ellipse. Recall that in ellip...
Hyperbola PRE-CALCULUS WEEK 6: 1ST QUARTER LEARNING OBJECTIVES: Define a hyperbola Transform standard equations of hyperbola into general form and vice versa Graph hyperbolas HYPERBOLA The definition of a hyperbola is similar to that of an ellipse. Recall that in ellipses, the sum of the distances between the foci and a point on the ellipse is fixed. In hyperbola, the difference of the distances between the foci and a point on the hyperbola is fixed. PARTS OF HYPERBOLA Equations of Hyperbola CASE 1. If the center of the hyperbola is at (h,k), the two forms of standard equation are as follows: Equation Transverse Axis Opening Horizontal Left and Right Upward and Vertical Downward Equations of Hyperbola CASE 2. If the center of the hyperbola is at the origin, the two forms of standard equation are as follows: Equation Transverse Axis Opening Horizontal Left and Right Upward and Vertical Downward Equations of Hyperbola CASE 2. If the center of the hyperbola is at the origin, the two forms of standard equation are as follows: Equation Transverse Axis Opening Horizontal Left and Right Upward and Vertical Downward ππππ‘ππππ : β Β± π, π πΆπ β ππππ‘ππππ : β, π Β± π Examples πΉπππ: β Β± π, π πΏπ 1&2: β + π, π Β± π2 π π2 π₯ 2 π¦ 2 πΏπ 3&4: β β π, π Β± π β =1 9 16 ππππ‘ππππ : β, π Β± π πΆπ β ππππ‘ππππ : β Β± π, π Examples πΉπππ: β, π Β± π π2 πΏπ 1&2: β Β± , π + π π π2 πΏπ 3&4: β Β± , π β π π¦ 2 π₯ 2 π β =1 16 4 ππππ‘ππππ : β Β± π, π πΆπ β ππππ‘ππππ : β, π Β± π Examples πΉπππ: β Β± π, π πΏπ 1&2: β + π, π Β± π2 π π2 πΏπ 3&4: β β π, π Β± (π¦ +2)2 (π₯ β 3)2 π β =1 16 9 ππππ‘ππππ : β, π Β± π πΆπ β ππππ‘ππππ : β Β± π, π Examples πΉπππ: β, π Β± π π2 πΏπ 1&2: β Β± , π + π π π2 πΏπ 3&4: β Β± , π β π 2 2 π (π₯ + 3) π¦ β =1 4 25 General to Standard 4π₯ 2 β 25π¦ 2 β 24π₯ β 64 = 0 Standard to General 2 2 π₯ π¦ β =1 25 11 General to Standard 3π₯ 2 β π¦ 2 + 18π₯ + 4π¦ + 35 = 0 Standard to General 2 2 (π₯ + 2) (π¦ + 1) β =1 4 9 Thank you