sketch a graph of $\\frac{x^{2}}{36}+\\frac{y^{2}}{25}=1$
sketch a graph of $\\frac{x^{2}}{36}+\\frac{y^{2}}{25}=1$
Answer
Explanation:
Step1: Identify the form of the equation
The equation (\frac{x^{2}}{36}+\frac{y^{2}}{25} = 1) is in the standard form of an ellipse (\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1), where (a^{2}=36), (b^{2} = 25). So (a = 6), (b=5).
Step2: Determine the vertices
For an ellipse (\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1) ((a>b)), the vertices on the (x) - axis are ((\pm a,0)) and the co - vertices on the (y) - axis are ((0,\pm b)). The vertices are ((6,0)) and ((-6,0)), and the co - vertices are ((0,5)) and ((0, - 5)).
Step3: Sketch the ellipse
Plot the vertices ((\pm6,0)) and co - vertices ((0,\pm5)) on the coordinate plane. Then draw a smooth curve passing through these four points to form the ellipse.
Answer:
Draw an ellipse with vertices ((6,0)), ((-6,0)) and co - vertices ((0,5)), ((0, - 5)) on the given coordinate grid.