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Question 251068: State whether the graph of each equation is a parabola, a circle, an ellipse, or a hyperbola. Then draw the graph. Show all work detailedly.
4x^2 - 26y^2 + 10 = 0
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
There is a 2nd degree x term AND a 2nd degree y term, so NOT a parabola.
The coefficients on the 2nd degree terms are different, so NOT a circle.
The 2nd degree x term has a different sign than the 2nd degree y term, so NOT an ellipse.
Therefore, hyperbola.
No first degree terms, so the center is at the origin. Put the constant term in the RHS then divide by the value of the constant term so that the RHS equals 1. After this operation, if the coefficient on  is positive, then the hyperbola opens east-west, otherwise north-south. The square root of the reciprocal of the coefficients on the 2nd degree terms give you the values  and  . For a north-south hyperbola centered at the origin, the vertices are at (0,b) and (0,-b)
John
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