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Question 173120: I'm struggling with a homework question.
Its reads as follows
Write an equation for each of the following.
a) The conic with center at the origin, focus a (0,-3) and e= 3/5
b) The conic centered at the origin with vertex at (2,0) and e=3/2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Write an equation for each of the following.
a) The conic with center at the origin, focus a (0,-3) and e= 3/5
Plot the center and the focus point.
Since e < 1 the conic is an ellipse.
Since the focus is below the center the form is
x^2/b^2 + y^2/a^2 = 1
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Since the distance from the center to the focus is 3, c=3.
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Since e = c/a = 3/5, a = 5
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Since a^2 = b^2+c^2, 25 = b^2 + 9
b = sqrt(16) = 4
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Equation:
x^2/16 + y^2/25 = 1
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b) The conic centered at the origin with vertex at (2,0) and e=3/2
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Plot the center and the vertex.
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Since e > 1 the conic is a hyperbola.
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Since the focus is to the right of the center,
the hyperbola opens to the right and to the left.
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Form: x^2/a^2 - y^2/b^2 = 1
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Distance from the center to the focus = c = 2.
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Since e = c/a = 3/2, a = 4/3
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Since c^2 = a^2+b^2, 4 = (4/3)^2 + b^2
b^2 = 4 - (16/9) = 20/9
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Equation:
x^2/(16/9) - y^2/(20/9) = 1
9x^2/16 - 9y^2/20 = 1
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Cheers,
Stan H.
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