Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Conics Review Sheet Pre-Calc. for AP Prep. Name: ___________ No Calculator 1. Find the coordinates of any points where the line x – y = 2 and the circle x 2 y 2 4 intersect. If necessary, note that the graphs are tangent or that they do not intersect. 2. Find the equation of the circle having (2, 5) and (-2, -1) as endpoints of a diameter. 3. Find the coordinates of the vertices and the foci of the ellipse with the equation 9 x 2 5 y 2 45 . Sketch the ellipse. 4. Find an equation for the ellipse that has (2, -4) and (2, 8) as its vertices and (5, 2) and (-1, 2) as endpoints of the minor axis. 5. Find an equation for the hyperbola that has a center at (0, 0), a vertex at (0, -3) and a focus at 0, 13 . 6. Find an equation of a hyperbola that has a vertex at (0, -3) and has asymptotes with equations 2 y x 5. 3 7. Find the coordinates of the vertex and focus and the equation of the directrix for the parabola x3 1 y 22 . 8 8. Sketch each of the following. Give the coordinates of the center, and for graphs other that circles, any foci, any vertices, and any asymptotes. a. 4 x 2 4 y 2 8x 24 y 15 0 b. y 2 x2 2 y 4x 4 0 9. A parabolic headlight has its bulb located at its focus, one inch from the vertex. If the total depth of the headlight is 2 inches, what is the diameter of the headlight? 10. Find the lengths of the minor and major axis of an ellipse that can be drawn using a string 8 feet long and two tacks anchored 1 foot apart from each other. Identify the conic section without completing the square. 11. 5x2 – 2xy + 5y2 – 12 = 0 12. 23x 2 26 3 xy 3 y 2 144 0 13. 4xy + 3y2 + 4x + 6y – 1 = 0 14. 10x2 + 24xy + 17y2 - 9 = 0 15. Graph the curves over the given interval 16. Graph the curves by eliminating the parameter. x = -sint y = -cost 0 < t < 2π x = 1 + 3 cost y = -1 + 2sint 0<t<π 17. Give two different sets of parametric equations for each rectangular equation. y = 4x3 + 5 Calculator Section Graph the following. 1. x 2 2 3 xy 3 y 2 12 3 x 12 y 0 2. 34x2 – 24xy + 41y2 – 25 = 0 Graph the following conics: 3. r 6 3 6sin 4. r 2 1 cos