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?

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) (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?
**
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".

RELATED QUESTIONS
find the vertices and asymptotes of the hyperbola. 9y 2 - 4x 2=36 need help with this (answered by robertb)

Find the vertices and asymptotes of the hyperbola. 9y^2 - 16x^2 =... (answered by lwsshak3)

find the equations of the asymptotes of the hyperbola x^2... (answered by lwsshak3)

-4x^2+9y^2-8x-54y+113=0, I need help in finding the CENTER,VERTICES,FOCI,and the equation (answered by MathLover1)

Find the slopes of the asymptotes of a hyperbola with the equation y� = 36 +... (answered by Edwin McCravy)

How do you find the center, vertices, foci, and asymptotes of the hyperbola?... (answered by lwsshak3)

Find the slopes of the asymptotes of the hyperbola with the equation 36 = 9x^2 �... (answered by ewatrrr)

Identify the vertices, foci, and slope of the asymptotes for the hyperbola x^2/25 -... (answered by lwsshak3)

Graph the equation. Identify the vertices, foci, and asymptotes of the hyperbola.... (answered by lwsshak3)