Description
graph the ellipse. Find the center, the lines which contain the major and minor axes, the vertices, the endpoints of the minor axis, the foci and the eccentricity for, x 2/ 9 + y 2 /25 = 1
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Explanation & Answer
The solutions are ready. Please ask if something is not clear.
0. Ellipse
𝑥2
9
𝑦2
+ 25 = 1.
Because the equation is in its canonical form
(𝑥−𝑥0 )2
𝑎2
+
(𝑦−𝑦0 )2
𝑏2
= 1, we know the minor
axis lies on 𝑦 = 0 and the major axis lies on 𝑥 = 0. Also we can easily find the center
(𝑥0 , 𝑦0 ) = (0, 0) and the endpoints of the minor axis (−3, 0) and (3, 0).
𝑎2
9
𝟒
To find the eccentricity we use the formula 𝑒 = √1 − 𝑏2 = √1 − 25 = 𝟓.
The foci are (0, ±√𝑏 2 − 𝑎2 ) = (𝟎, ±𝟒).
The graph is on the picture.
sin 𝑥
1. sin(2𝑥) = tan 𝑥, or 2 sin 𝑥 cos 𝑥 = cos 𝑥. Note that cos 𝑥 must be nonzero and
1
remember that sin 𝑥 = 0, or 𝑥 = 𝑘𝜋, are solutions. Thus, we obtain 2 cos 𝑥 = cos 𝑥, or
1
1
cos2 𝑥 = 2 , cos 𝑥 = ±
𝜋
. We know such angles, they are 𝑥 = 4 +
√...
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