To Find: The center, vertices, and foci of the ellipse.
Center of the ellipse
Given information:
The equation of ellipse is
Calculation:
The standard form of the ellipse equation is
Rewrite
Therefore, the ellipse properties are:
Ellipse with center
The vertices are the two points on the ellipse that intersect the major axis. For an ellipse with major axis parallel to the
Compare the equation with standard equation of ellipse:
Ellipse with center
Thus, the vertices of the ellipse are
Calculate the value of
The foci of the ellipse are defined as
Thus, the foci are
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
- 16. Solve each of the following equations for x. (a) 42x+1 = 64 (b) 27-3815 (c) 92. 27² = 3-1 (d) log x + log(x - 21) = 2 (e) 3 = 14 (f) 2x+1 = 51-2xarrow_forward11. Find the composition fog and gof for the following functions. 2 (a) f(x) = 2x+5, g(x) = x² 2 (b) f(x) = x²+x, g(x) = √√x 1 (c) f(x) = -1/2) 9 9(x) = х = - Xarrow_forwardpractice problem please help!arrow_forward
- 13. A restaurant will serve a banquet at a cost of $20 per person for the first 50 people and $15 for person for each additional person. (a) Find a function C giving the cost of the banquet depending on the number of people p attending. (b) How many people can attend the banquet for $2000?arrow_forwardAlt Fn Ctrl 12. Find functions f and g such that h(x) = (fog)(x). (a) h(x) = (x² + 2)² x+1 (b) h(x) = 5 3arrow_forward15. Find the exact value. (a) log4 16 (b) log7 1 49 (c) logs 3/25arrow_forward
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