Graph (x^2)/49+(y^2)/24=1

Problem

(x2)/49+(y2)/24=1

Solution

1. Identify the type of conic section. Since the equation is in the form (x2)/(a2)+(y2)/(b2)=1 with positive coefficients, it is an ellipse centered at the origin (0,0)

2. Determine the semi-major and semi-minor axes. Here a2=49 and b2=24 Taking the square roots gives a=7 and b=√(,24)=2√(,6)≈4.9

3. Locate the vertices and co-vertices. Since a>b the major axis is horizontal. The vertices are at (±7,0) and the co-vertices are at (0,±2√(,6))

4. Calculate the foci using the relationship c2=a2−b2

c2=49−24

c2=25

c=5

The foci are located at (±5,0)

5. Sketch the graph by plotting the center (0,0) the vertices (±7,0) and the co-vertices (0,±4.9) then drawing a smooth curve through these points.

Final Answer

(x2)/49+(y2)/24=1* is an ellipse with vertices *(±7,0)* and co-vertices *(0,±2√(,6))

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