6 Find the Standard vertices 0 of the hyperbola with vertice

6. Find the Standard vertices (0 of the hyperbola with vertices (0.13) and with the equation asymptotes y tir. 7. Use a graphing utility to graph the conic 1. Describe your viewing window. 8. (a) Determine the number of degrees the axis must be rotated to eliminate the ay-term of the conic 6ay 6 0. (b) Graph the conic in part (a) and use a graphing utility to confirm your result. 9. Solve the system of equations at the right algebraically by the method of substitution. Then verify your results by using a graphing utility. System for 9 x+ y 5 0

Solution

6) Solution :

The transverse axis is parallel to the y-axis (the positive part of this equation.
(h, k) is the center ... (0, 0)
a = distance from the center to the vertices along the transverse axis
b = distance from the center to the endpoints of the conjugate axis
c = distance from the center to the foci along the transverse axis
Given: a = 3
The relationship between a, b, and c is
3² + b² = c²

The slope of the asymptotes is ±3/2
a = is a multiple of 3
b = is a multiple of 2 ... be careful not to always assume that a=3 and b = 2.
For this problem a = 3
hence, b = 4

3² + 4² = c²
25 = c²
c = 5

Summary
center = (0, 0)
a² = 9
b² = 16
c² = 25
transverse axis x = 0
equation of the hyperbola

[y²/3²] - [x²/4²] = 1