Hyperbola Pre-Calculus PDF

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  𝑉𝑒𝑟𝑡𝑖𝑐𝑒𝑠: ℎ ± 𝑎, 𝑘 𝐶𝑜 − 𝑉𝑒𝑟𝑡𝑖𝑐𝑒𝑠: ℎ, 𝑘 ± 𝑏 Examples 𝐹𝑜𝑐𝑖: ℎ ± 𝑐, 𝑘 𝐿𝑅 1&2: ℎ + 𝑐, 𝑘 ± 𝑏2 𝑎 𝑏2 𝑥 2 𝑦 2 𝐿𝑅 3&4: ℎ − 𝑐, 𝑘 ± 𝑎 − =1 9 16  𝑉𝑒𝑟𝑡𝑖𝑐𝑒𝑠: ℎ, 𝑘 ± 𝑎 𝐶𝑜 − 𝑉𝑒𝑟𝑡𝑖𝑐𝑒𝑠: ℎ ± 𝑏, 𝑘 Examples 𝐹𝑜𝑐𝑖: ℎ, 𝑘 ± 𝑐 𝑏2 𝐿𝑅 1&2: ℎ ± , 𝑘 + 𝑐 𝑎 𝑏2 𝐿𝑅 3&4: ℎ ± , 𝑘 − 𝑐 𝑦 2 𝑥 2 𝑎 − =1 16 4  𝑉𝑒𝑟𝑡𝑖𝑐𝑒𝑠: ℎ ± 𝑎, 𝑘 𝐶𝑜 − 𝑉𝑒𝑟𝑡𝑖𝑐𝑒𝑠: ℎ, 𝑘 ± 𝑏 Examples 𝐹𝑜𝑐𝑖: ℎ ± 𝑐, 𝑘 𝐿𝑅 1&2: ℎ + 𝑐, 𝑘 ± 𝑏2 𝑎 𝑏2 𝐿𝑅 3&4: ℎ − 𝑐, 𝑘 ± (𝑦 +2)2 (𝑥 − 3)2 𝑎 − =1 16 9  𝑉𝑒𝑟𝑡𝑖𝑐𝑒𝑠: ℎ, 𝑘 ± 𝑎 𝐶𝑜 − 𝑉𝑒𝑟𝑡𝑖𝑐𝑒𝑠: ℎ ± 𝑏, 𝑘 Examples 𝐹𝑜𝑐𝑖: ℎ, 𝑘 ± 𝑐 𝑏2 𝐿𝑅 1&2: ℎ ± , 𝑘 + 𝑐 𝑎 𝑏2 𝐿𝑅 3&4: ℎ ± , 𝑘 − 𝑐 2 2 𝑎 (𝑥 + 3) 𝑦 − =1 4 25 General to Standard 4𝑥 2 − 25𝑦 2 − 24𝑥 − 64 = 0 Standard to General 2 2 𝑥 𝑦 − =1 25 11 General to Standard 3𝑥 2 − 𝑦 2 + 18𝑥 + 4𝑦 + 35 = 0 Standard to General 2 2 (𝑥 + 2) (𝑦 + 1) − =1 4 9 Thank you