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.Com
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)   (Show Source): You can put this solution on YOUR website!
Notice how there is no 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.

Start with the given equation


Subtract 18x from both sides


Rearrange the terms


Rearrange the equation


Divide both sides by 4 to isolate "y"


Break up the fraction


Reduce


So this equation fits the general second degree polynomial which means that it is a parabola. If we graph , we get

Graph of

So this confirms our answer.

RELATED QUESTIONS

I need to identify the type of conic section x^2+5xy-4y^2=10 A) circle B)... (answered by MathLover1)
18. Classify the conic section of the equation x^2 + 2x + y^2 + 6y = 15. A circle B... (answered by jim_thompson5910)
which conic section is formed by the followin equation 4y^2=-4x^2+36 (answered by solver91311)
Which type of conic section is represented by the equation: (x-3)^2 + (y+1)^2 = 9 A.... (answered by stanbon)
Determine the type of conic section represented by the equation (X+6)^2/25 - (y+4)^2/64 (answered by ikleyn)
Classify the conic section 5x^2 + 9y^2 = 45 A line B point C circle D parabola... (answered by jim_thompson5910)
Classify the conic section x^2 + y^2 = 121 A hyperbola B ellipse C point D... (answered by jim_thompson5910)
What conic does the equation 4x^2+4y^2=16 represent? A. Circle C. Parabola (answered by vertciel)
Classify the conic section: 1. x^2 + y^2 = 36 A point B ellipse C circle D... (answered by jim_thompson5910)