X square + y square= 9. Is it circle, ellipse, parabola, hyperbola

Question

choose the correct conic section to the equation

x square + y square =9

Answer 1

 This is a circle with radius R = 3 centered in the origin of a coordinate system. Equation of these circles with the radius R is 

                                                    x² + y² = R ²

R² = 9. Thus, R = 3. Equations for ellipse, parabola, and hyperbola are different from this one, but they all belong to the family of conic sections.

 

Answer 2

 

 X²  +y^{2 =} r²

 

 If coefficients of X² ,Y²   are equal, like here that is = 1,   Circle

 

 2X² + 3Y ²  = r^{2  ,}    coefficients  of X^{2 ,} Y²  are different, (2,3 here) ,  Ellipse

 

 X² - Y² = r²  , or  Y² - X² = r²    ( Hyperbola)

 

aX² = Y or ay² = X  , then ( Parabola).  ,

 

 

Answer 3

Hey Shaunice!

With parabolas, only ONE term is squared: x^2 + y  OR  y^2 + x ...

With circles, BOTH terms are squared, added in equal proportions: x^2 + y^2 ...

With ellipses, terms are squared, added in different scalings: Ax^2 + By^2 ...

With hyperbolas, BOTH terms are squared, but "counteract" (minus) each other: Ax^2 - By^2 ...

Best wishes :)