SOLUTION: Find the equation of asymptotes of the hyperbola 9y^2-4x^2=36 and obtain the product of the perpendicular distances between any point of the hyperbola and the asymptotes?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of asymptotes of the hyperbola 9y^2-4x^2=36 and obtain the product of the perpendicular distances between any point of the hyperbola and the asymptotes?       Log On


   

Question 659135: Find the equation of asymptotes of the hyperbola 9y^2-4x^2=36 and obtain the product of the perpendicular distances between any point of the hyperbola and the asymptotes?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of asymptotes of the hyperbola 9y^2-4x^2=36 and obtain the product of the perpendicular distances between any point of the hyperbola and the asymptotes?
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9y^2-4x^2=36
y^2/4-x^2/9=1
This is an equation of a hyperbola with vertical transverse axis
center: (0,0)
a^2=4
a=2
b^2=9
b=3
slopes of asymptotes: ±a/b=±2/3
equations of asymptotes: y=2x/3 and y=-2x/3
..
The line representing the perpendicular distance between any point of the hyperbola and the asymptotes has a slope=negative reciprocal of the asymptotes=±3/2. Since slope=∆y/∆x, the distance formula can be used to determine the perpendicular distance. I'm not sure what is meant by "product of perpendicular distances".