Advanced Geometry Conic Sections Lesson 4

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Presentation transcript:

Advanced Geometry Conic Sections Lesson 4 Ellipses & Hyperbolas

Ellipses Minor Axis Definition – the set of all points in a plane that the sum of the distances from two given points, called the foci, is constant V Major Axis F C F V V V

Equation (a² > b²) Center Foci equation vertices Major Axis Minor Axis

Example: For the equation of each ellipse or hyperbola, find all information listed. Then graph. Center: Foci: Length of the major axis: minor axis:

Hyperbola Definition – the set of all points in a plane that the absolute value of the distance from two given points in the plane, called the foci, is constant Asymptote F V Conjugate Axis C V Asymptote F Transverse Axis

Equation of a Hyperbola Slopes of the Asymptotes Center Foci Vertices Slopes of the Asymptotes Direction of Opening

Example: For the equation of each ellipse or hyperbola, find all information listed. Then graph. Center: Vertices: Foci: Slopes of the asymptotes:

Example: Using the graph below, write the equation for the ellipse or hyperbola.

Example: Using the graph below, write the equation for the ellipse or hyperbola.

Write the equation of the ellipse or hyperbola that meets Example: Write the equation of the ellipse or hyperbola that meets each set of conditions. The foci of an ellipse are (-5, 3) and (3, 3) and the minor axis is 6 units long.

Write the equation of the ellipse or hyperbola that meets Example: Write the equation of the ellipse or hyperbola that meets each set of conditions. The vertices of a hyperbola are (0,-3) and (0, -8) and the length of the conjugate axis is units long.

Example: Write each equation in standard form. Determine if it is an ellipse or a hyperbola.