graph each equation.\n9) $\frac{x^2}{4} + \frac{y^2}{9} = 1$
graph each equation.\n9) $\frac{x^2}{4} + \frac{y^2}{9} = 1$
Answer
Explanation:
Step1: Identify the form of the equation
The equation (\frac{x^{2}}{4}+\frac{y^{2}}{9} = 1) is in the standard form of an ellipse (\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1) ((a>b>0)). Here (a^{2} = 9), so (a = 3); (b^{2}=4), so (b = 2).
Step2: Determine the vertices and co - vertices
For an ellipse of the form (\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1), the vertices are ((0,\pm a)) and the co - vertices are ((\pm b,0)). Substituting (a = 3) and (b = 2), the vertices are ((0,3)) and ((0, - 3)), and the co - vertices are ((2,0)) and ((-2,0)).
Step3: Sketch the ellipse
Plot the vertices ((0,3)), ((0, - 3)), co - vertices ((2,0)) and ((-2,0)). Then draw a smooth curve passing through these four points to form the ellipse.
Answer:
The ellipse has vertices ((0,3)) and ((0, - 3)), co - vertices ((2,0)) and ((-2,0)). Sketch the ellipse by connecting these four points with a smooth curve.