SOLUTION: 20. Classify the conic section of the equation 9x^2 - 3 = 18x + 4y. A hyperbola B circle C ellipse D line E Graph is not a conic section. F parabola I'm not sure wher

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 20. Classify the conic section of the equation 9x^2 - 3 = 18x + 4y. A hyperbola B circle C ellipse D line E Graph is not a conic section. F parabola I'm not sure wher      Log On


   

Question 162033: 20. Classify the conic section of the equation 9x^2 - 3 = 18x + 4y.
A hyperbola
B circle
C ellipse
D line
E Graph is not a conic section.
F parabola
I'm not sure where to start, I really would apperciate your help with how to solve this to come to the correct answer. Thank you so much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice how there is no y%5E2 term. So this means that the equation is NOT a circle, ellipse, or hyperbola. So it's either a line or a parabola. However, let's use some algebra to find out for sure.

9x%5E2+-+3+=+18x+%2B+4y Start with the given equation


9x%5E2+-+3-18x+=+4y Subtract 18x from both sides


9x%5E2+-18x-+3+=+4y Rearrange the terms


4y=9x%5E2+-18x-+3 Rearrange the equation


y=%289x%5E2+-18x-+3%29%2F4 Divide both sides by 4 to isolate "y"


y=%289x%5E2%29%2F4+-%2818x%29%2F4-+%283%29%2F4 Break up the fraction


y=%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4 Reduce


So this equation fits the general second degree polynomial which means that it is a parabola. If we graph y=%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4, we get

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4%29+ Graph of y=%289%2F4%29x%5E2+-%289%2F2%29x-+3%2F4

So this confirms our answer.