Advanced Geometry Conic Sections Lesson 4 Ellipses Hyperbolas

Advanced Geometry Conic Sections Lesson 4 Ellipses & Hyperbolas

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

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

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

Hyperbola Asymptote F C Asymptote V V F Transverse Axis Conjugate Axis 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

Equation of a Hyperbola 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: 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.

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.