INSTRUCTION Sketch the graph and label all the parameters. Determine all the necessary parameters A. Center B. Foci C. Ends of Latus Rectum D. Standard Equation E. General Equation 1. An ellipse is defined by parametric equations as follows: x= 5 sin (b) y= 7 cos (b) 2. Find the equation of the focus of points P(x, y) whose sum of its distances from the two fixed points (4,-2) and (-2,2) is equal to 8. 3. Determine the equation of the ellipse centered at (0,0) knowing that one of its vertices is 8 units from a focus and 18 units from the other.

INSTRUCTION Sketch the graph and label all the parameters. Determine all the necessary parameters A. Center B. Foci C. Ends of Latus Rectum D. Standard Equation E. General Equation 1. An ellipse is defined by parametric equations as follows: x= 5 sin (b) y= 7 cos (b) 2. Find the equation of the focus of points P(x, y) whose sum of its distances from the two fixed points (4,-2) and (-2,2) is equal to 8. 3. Determine the equation of the ellipse centered at (0,0) knowing that one of its vertices is 8 units from a focus and 18 units from the other.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.4: Plane Curves And Parametric Equations

Problem 68E

See similar textbooks

Similar questions

Shooting into the Wind Suppose that a projectile is fired into a headwind that pushes it back so as to reduce its horizontal speed by a constant amount . Find parametric equations for the path of the projectile.
If the directrix of a conic section is perpendicular to the polar axis, what do we know about the equation of the graph?
If a conic section is written as a polar equation, what must be true of the denominator?
Epicycloid If the circle C of Exercise 63 rolls on the outside of the larger circle, the curve traced out by P is called an epicycloid. Find parametric equations for the epicycloid. Hypocycloid A circle C of radius b rolls on the inside of a larger circle of radius a centered at the origin. Let P be a fixed point on the smaller circle, with the initial position at the point (a,0) as shown in the figure. The curve traced out by P is called a hypocycloid. a Show that parametric equations of hypocycloid are x=(ab)cos+bcos(abb) y=(ab)sinbsin(abb) b If a=4b, the hypocycloid is called an asteroid. Show that in this case parametric equations can be reduced to x=acos3y=asin3 Sketch the curve. Eliminate the parameter to obtain an equation for the asteroid in rectangular coordinates.
A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 50 feet and a height at the center of 10 feet. (a) Sketch the arch of the tunnel on a rectangular coordinate system with the center of the road entering the tunnel at the origin. Label the coordinates of the known points. (b) Find an equation of the semielliptical arch over the tunnel. (c) You are driving a moving truck that has a width of 8 feet and a height of 9 feet. Will the moving truck clear the opening of the arch?