SOLUTION: 15. find the standard form of the equation of the ellipse with center at the origin, vertices at the origin, vertices at (+/-5,0) and foci at (+/-3,0) 16. Find the standard fo

Question 600133: 15. find the standard form of the equation of the ellipse with center at the origin, vertices at the origin, vertices at (+/-5,0) and foci at (+/-3,0)
16. Find the standard form of the ellipse with center at the origin, vertices at (0,+/-4), and minor axis of length 6.
17. Find the standard form of the equation of the ellipse with vertices at (-2,3) and (6,3) and major axis of length 12.
18. find the standard form of the equation of the ellipse with vertices at (5,-2) and (-7,-2) and minor axis of length 4.
19. Find the standard form of the equation of the ellipse with minor axis of length 6, center at (5,-1) and a focus at (-1,-1).
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
15. find the standard form of the equation of the ellipse with center at the origin, vertices at (+/-5,0) and foci at (+/-3,0)
19. Find the standard form of the equation of the ellipse with minor axis of length 6, center at (5,-1) and a focus at (-1,-1).
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I will do problems 15 and 19. Problems 16, 17, and 18 are similar to 15
15. find the standard form of the equation of the ellipse with center at the origin, vertices at (+/-5,0) and foci at (+/-3,0)
This is an ellipse with horizontal major axis.
Its standard form of equation: (x-h)^2+(y-k)^2=1, a>b, (h,k)=(x,y) coordinates of center.
For given ellipse:
center(0,0)
a=5
a^2=25
c=3
c^2=9
c^2=a^2-b^2
b^2=a^2-c^2
b^2=25-9=16
Equation for given ellipse:
x^2/25+y^2/z16=1
..
19. Find the standard form of the equation of the ellipse with minor axis of length 6, center at (5,-1) and a focus at (-1,-1).
This is an ellipse also with horizontal major axis.
Its standard form of equation: (x-h)^2+(y-k)^2=1, a>b, (h,k)=(x,y) coordinates of center.
For given ellipse:
center: (5,-1)
2b=6
b=3
b^2=9
c=(5-1/2=4/2=2
c^2=4
c^2=a^2-b^2
a^2=c^2+b^2=4+9=13
a^2=13
a≈√13≈3.6
Equation for given ellipse:
(x-5)^2/13+(y+1)^2/9=1

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