Graph 4x^2+25y^2=100

Problem

4*x^2+25*y^2=100

Solution

1. Identify the type of conic section by observing that both x^2 and y^2 terms are positive and have different coefficients, which indicates an ellipse.

2. Divide both sides of the equation by 100 to put the equation into the standard form of an ellipse, (x^2)/(a^2)+(y^2)/(b^2)=1

(4*x^2)/100+(25*y^2)/100=100/100

3. Simplify the fractions to find the values of a^2 and b^2

(x^2)/25+(y^2)/4=1

4. Determine the center and the intercepts. The center is at the origin (0,0) Since a^2=25 the x-intercepts are (±5,0) Since b^2=4 the y-intercepts are (0,±2)

5. Sketch the graph by plotting the vertices at (5,0) and (−5,0) and the co-vertices at (0,2) and (0,−2) then drawing a smooth oval connecting these points.

Final Answer

(x^2)/25+(y^2)/4=1

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