71 THE DISTANCE AND MIDPOINT FORMULAS

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7-1 THE DISTANCE AND MIDPOINT FORMULAS

• Formulas
• Distance
• Midpoint
• Distance formula proof
• Examples
• (-5, 3), (-3, -7)
• (-7, 3), (a, 11), d10

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7-2 PARABOLAS

• Define
• Conic Sections
• Focus
• directrix
• Parabola
• Latus Rectum

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• B. Using y a(x-h)2 k
• Axis of symmetry x h
• Vertex (h, k)
• Focus (h, k )
• Directrix y k
• Up or down a or a
• Latus rectum length
• C. Example x y2 12y 20

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7-3 CIRCLES

• Define
• Circle
• Center
• Radius
• Equation of a Circle

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• C. Examples
• Write the equation
• (0, 3) r 7
• Find the center, radius, and graph the circle.
• (x3)2 (y7)2 81
• 4x2 4y2 36y 5 0

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7-4 ELLIPSES

• Define
• Ellipse 3. Minor Axis
• Major Axis 4. Center
• Standard Equations with center at origin

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• C. Standard Equations with center at (h, k)

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7-5 HYPERBOLAS

• Define
• Hyperbola 4. Asymptotes
• Center 5. Transversal Axis
• Vertex 6. Conjugate Axis
• Standard Equations with center at origin

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• C. Standard Equations with center at (h, k)
• D. Steps
• Change into standard form
• Find center
• Find vertex
• Find asymptotes
• Find foci
• Graph hyperbola

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• Example
• 1.
• 2. (x 3)2 4(y 2)2 4

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7-6 CONIC SECTIONS

• Equation of a conic section
• Relationship of A and C (P.451)
• B. Standard Form of Equations
• Parabola 3. Ellipse
• Circle 4. Hyperbola

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• C. Examples
• x2 y2 6y 13 36
• 4x2 2y2 8
• y 4 (x 2)2