graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
graph each equation. 9) \\(\\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: Find the vertices
For the ellipse (\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1), the vertices on the (y -)axis are ((0,\pm a)). Substituting (a = 3), the vertices are ((0,3)) and ((0, - 3)).
Step3: Find the co - vertices
The co - vertices on the (x -)axis are ((\pm b,0)). Substituting (b = 2), the co - vertices are ((2,0)) and ((-2,0)).
Step4: 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)). Plot these points and draw the ellipse.