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Solution of exercise 6 determine the equation of the hyperbola centered at 0 0 that passes through the points.
Hyperbola examples and solutions math. Since the transverse axis is horizontal the standard form of the hyperbola is or. X 2 4 2 1. We now compare the equation obtained with the standard equation left in the review above and we can say that the given equation is that of an hyperbola with a 4 and b 3. X 3 2 4 y 1 2 9 1 x 3 2 4 y 1 2 9 1 solution.
3 x 1 2 y 1 2 2 1 3 x 1 2 y 1 2 2 1 solution. In the graph 2 c 6 and 2 a 4 or c 3 a 2. Y2 16 x 2 2 9 1 y 2 16 x 2 2 9 1 solution. For problems 1 3 sketch the hyperbola.
C2 a2 b2 pythagorean relation step 3. Displaystyle y 2 frac x 2 3 1 y2 3x2. A more formal definition of a hyperbola is a collection of all points whose distances to two fixed points called foci plural for. Set y 0 in the equation obtained and find the x intercepts.
A hyperbola can open to the left and right or open up and down. X 2 16 y 2 9 1. Y 2 x 2 3 1. 9 4 b2 substitute 3 for c 2 for a step 4.
Notice that it is not a function since for each x value there are two y values. X 2 4 2 y 2 3 2 1.
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