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Question 726171: Write the equation x^2+8y^2-14x-15=0 in the standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Write the equation x^2+8y^2-14x-15=0 in the standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation.
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Both the x^2 and y^2 are present so it is ellipse or hyperbola
The sign of the coefficients are the same so it is an ellipse.
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Complete the square on the x and on the y terms.
x^2 -14x + 49 + 8(y^2) = 15+49
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Factor:
(x-7)^2 + 8(y-0)^2 = 64
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Standardize
(x-7)^2/8^2 + (y-0)^2/(sqrt(8))^2 = 1
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Center: (7,0)
Semi major axis: 8 (horizontal)
Semi minor axis: 2sqrt(2) (vertical)
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Cheers,
Stan H.
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