Working With Hyperbolas(you have to know where to look)

urban geometry hyperbolas by flickr user johncarney

Horizontal Hyperbola Vertical Hyperbola

Oab O

ab

The Pythagorean Property

b2c2 a2+=A1

B1

A2 F1F2B2

Horizontal Hyperbola Vertical Hyperbola

Oab

cc

a

The Pythagorean Property

b2c2 a2+=

Horizontal Hyperbola Vertical Hyperbola

O

ab

Oab

For the hyperbola whose equation is given below.(i) Write the equation in standard form(ii) Determine the lengths of the transverse and conjugate axes,

the coordinates of the verticies and foci, and the equations of the asymptotes.

(iii) Sketch a graph of the hyperbola.HOMEWORK

For the hyperbola whose equation is given below.

(i) Write the equation in standard form(ii) Determine the lengths of the transverse and conjugate axes,

the coordinates of the verticies and foci, and the equations of the asymptotes.

(iii) Sketch a graph of the hyperbola.SLOPE INTERCEPT FORM

For the hyperbola whose equation is given below.

(i) Write the equation in standard form(ii) Determine the lengths of the transverse and conjugate axes,

the coordinates of the verticies and foci, and the equations of the asymptotes.

(iii) Sketch a graph of the hyperbola.SLOPE INTERCEPT FORM

The foci of a hyperbola are F (6, 0) and F (-6, 0), and the difference of the focal radii is 4 units. Use the definition of a hyperbola to derive the equation of this hyperbola.

21

A rock is kicked off a vertical cliff and falls in a parabolic path to the water below. The cliff is 40 m high and the rock hits the water 10 m from the base of the cliff. What is the horizontal distance of the rock from the cliff face when the rock is at a height of 30 m above the water?

The cross section of the roof of an indoor tennis court has a semi elliptical shape. If the roof spans 86 m and has a height of 30 m, find the height of the roof 20 m from the centre A. HOMEWORK

Sketch the graph, identify the vertex, focus, equation of the axis of symmetry and the equation of the directrix. HOMEWORK

A hyperbola has vertices at (1, -4) and (1, 8). If the asymptotes have slopes ±2, determine the equation of the hyperbola in standard form.

HOMEWORK

For each ellipse whose equation is given below(i) Write the equation in standard form(ii) Determine the lengths of the major and minor axes, the

coordinates of the verticies, and the coordinates of the foci.(iii) Sketch a graph of the ellipse.

HOMEWORK

Determine the equation of a parabola defined by the given conditions.The vertex is V(-1, 3) and the equation of the directrix is x - 2 = 0

HOMEWORK

The cross section of a drainage ditch is parabolic in shape, as shown in the diagram at the right. When the width of the water surface is 10 m, the maximum depth of the water is 1.5 m. Determine the width of the water, w, when the maximum depth is 3 m.

HOMEWORK

For each ellipse whose equation is given below(i) Write the equation in standard form(ii) Determine the lengths of the major and minor axes, the

coordinates of the verticies, and the coordinates of the foci.(iii) Sketch a graph of the ellipse.

HOMEWORK