Solution Found!
Answer: Equations of hyperbolas Find an equation of the
Chapter 9, Problem 47E(choose chapter or problem)
Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work.
A hyperbola with vertices \((\pm2,\ 0)\) and asymptotes \(y=\pm3x/2\)
Questions & Answers
QUESTION:
Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work.
A hyperbola with vertices \((\pm2,\ 0)\) and asymptotes \(y=\pm3x/2\)
ANSWER:Solution 47EStep 1:In this problem we need to find an equation of the hyperbolas, assuming the center is at the origin.Given A hyperbola with vertices (±2, 0) and asymptotes y = ±3x/2The standard form of the equation of a hyperbola with center (0,0) and transverse axis on the x-axis iswhere* the length of the transverse axis is 2a* the coordinates of the vertices are (±a,0) * the length of the conjugate axis is 2b * the coordinates of the co-vertices are (0,±b)* the distance between the foci is 2c, where * the coordinates of the foci are (±c,0)* the equations of the asymptotes are