SOLUTION: 1) 4X^2+3x+5Y+6=0 2) 2x^2+3x+4y^2-5y-6=1 I need help figuring out what theses ellipse formulas would be and how to get them into standard form. Thank you

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 1) 4X^2+3x+5Y+6=0 2) 2x^2+3x+4y^2-5y-6=1 I need help figuring out what theses ellipse formulas would be and how to get them into standard form. Thank you      Log On


   

Question 1108327: 1) 4X^2+3x+5Y+6=0
2) 2x^2+3x+4y^2-5y-6=1
I need help figuring out what theses ellipse formulas would be and how to get them into standard form. Thank you
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
1) #1 is not an ellipse. It is a parabola, instead.


2) #2 is an ellipse.

You should apply "completing the squares" procedure to get the ellipse equation in the standard form.

The best place to learn it from are my lessons
    - Ellipse definition, canonical equation, characteristic points and elements

    - Standard equation of an ellipse
    - Identify elements of an ellipse given by its standard equation
    - Find the standard equation of an ellipse given by its elements

    - General equation of an ellipse
    - Transform a general equation of an ellipse to the standard form by completing the square (*)
    - Identify elements of an ellipse given by its general equation
in this site.

Your major source is the lesson marked  (*)  in the list.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.