SOLUTION: state which type of conic section each equation represents. then put the equation into standard form. x^2+9y^2-4x+54y+49=0

Question 281466: state which type of conic section each equation represents. then put the equation into standard form.
x^2+9y^2-4x+54y+49=0
Answer by Mathematicians(84) (Show Source): You can put this solution on YOUR website!

The key points on this on is that you have a positive and a positive , you only have two choices on what this could be, either a circle or ellipse. However, the coefficient near the y^2 has a 9 while the x^2 has a 1, so it cannot be a circle (otherwise they would be the same).
To put it in standard form, you will heavily use the completing the square method.

subtract 49 on both sides
group the x's and y's together

You will notice I put +_ and -_ in each of those answers, that is because whenever you add and subtract the same number, you get 0, so you can do that in this case. The number you will add will be whatever half the term near the x or y and square it. For example, for the 4x I got the 9 doing the same method as above. From here, we can add 4 to both sides and add 81 to both sides. Why 81? Well the -9 is inside parenthesis and in order to get it out, you need to distribute the 9 from outside then add it over to the right side

Finally do some factoring:

Divide 36 on both sides and you get:

Which simplifies to

This is in standard form, you didn't need to write the 6^2, this makes it easier to see the major and minor axis of the ellipse.
RELATED QUESTIONS
help me put this equation into standard form and solve the conic:... (answered by stanbon)

i have to write the equation of the conic section in standard form and classify the conic (answered by solver91311)

Classify the conic section and write its equation in standard form.... (answered by Big Poop)

write an equation of the conic section parabola with vertex at (2,6) and directrix at... (answered by lwsshak3)

find the standard form of the equation 196x^2+9y^2+392x+54y-1487=0 by completing the... (answered by ewatrrr)

Hi! My directions are, "Use completing the square to write the equation of each conic... (answered by josgarithmetic)

find the standard form of each equation by completing the square then identify the conic... (answered by lwsshak3)

write the equation in standard form. name the center, the length of the minor and major... (answered by lwsshak3)

Find the center, vertices, and foci of the hyperbola and put the equation in standard... (answered by lwsshak3)