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# Pre-Cal 40S May 26, 2009

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Applications of conics.

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### Pre-Cal 40S May 26, 2009

1. 1. Working With Hyperbolas (you have to know where to look) urban geometry hyperbolas by ﬂickr user johncarney
2. 2. Horizontal Hyperbola Vertical Hyperbola a b b O a O
3. 3. The Pythagorean Property B1 2 2 2 b c c = a +b A2 a a A1 F2 O c F1 B2 Horizontal Hyperbola Vertical Hyperbola
4. 4. The Pythagorean Property 2 2 2 c = a +b a b b O a O Horizontal Hyperbola Vertical Hyperbola
5. 5. 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. HOMEWORK (iii) Sketch a graph of the hyperbola.
6. 6. 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. SLOPE INTERCEPT FORM (iii) Sketch a graph of the hyperbola.
7. 7. 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. SLOPE INTERCEPT FORM (iii) Sketch a graph of the hyperbola.
8. 8. The foci of a hyperbola are F (6, 0) and F (-6, 0), and the difference of 1 2 the focal radii is 4 units. Use the deﬁnition of a hyperbola to derive the equation of this hyperbola.
9. 9. 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?
10. 10. 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
11. 11. Sketch the graph, identify the vertex, focus, equation of the axis of symmetry and the equation of the directrix. HOMEWORK
12. 12. 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
13. 13. For each ellipse whose equation is given below (i) Write the equation in standard form HOMEWORK (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.
14. 14. 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
15. 15. The cross section of a HOMEWORK 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.
16. 16. For each ellipse whose equation is given below (i) Write the equation in standard form HOMEWORK (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.
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