SOLUTION: Classify the conic section 5x^2 + 9y^2 = 45 A line B point C circle D parabola E ellipse F hyperbola I believe the answer is E. But I am not 100% sure, and Id love

Algebra.Com
Question 161956: Classify the conic section
5x^2 + 9y^2 = 45
A line
B point
C circle
D parabola
E ellipse
F hyperbola

I believe the answer is E. But I am not 100% sure, and Id love to know if that is correct, and if not, what is? Thank you so much for your time.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation

Replace "x" with "x-0" and replace "y" with "y-0". This is valid since adding/subtracting zero doesn't change the equation.


Divide EVERY term by 45 to make the right side equal to 1.


Reduce


Take note that and


Replace "9" with . Replace "5" with


Remember, the equation of any ellipse is .

Since the equation fits this format where , , , and , this shows us that the equation is an ellipse.

So you are correct. Once again you can use a graph to verify your answer.

RELATED QUESTIONS

Classify the conic section x^2 + y^2 = 121 A hyperbola B ellipse C point D... (answered by jim_thompson5910)
Classify the conic section: x^2 - y^2 = 36 A circle B hyperbola C parabola D... (answered by jim_thompson5910)
20. Classify the conic section of the equation 9x^2 - 3 = 18x + 4y. A hyperbola B... (answered by jim_thompson5910)
18. Classify the conic section of the equation x^2 + 2x + y^2 + 6y = 15. A circle B... (answered by jim_thompson5910)
Classify the conic section: 1. x^2 + y^2 = 36 A point B ellipse C circle D... (answered by jim_thompson5910)
I need to identify the type of conic section x^2+5xy-4y^2=10 A) circle B)... (answered by MathLover1)
Determine the type of conic section represented by the equation (X+6)^2/25 - (y+4)^2/64 (answered by ikleyn)
Choose the correct conic section to fit the equation. 49x^2 - 16y^2 = 784 a.)circle... (answered by Fombitz)
Which type of conic section is represented by the equation: (x-3)^2 + (y+1)^2 = 9 A.... (answered by stanbon)