Question

13 x²+6 √3 x y+7 y²=16 Sketch the graph.

Answer 1

To sketch the graph of the equation 13x²+6√3xy+7y²=16, follow these steps: isolate variables, identify the conic section, analyze coefficients, and plot the graph of an ellipse.

Step-by-step explanation:

To sketch the graph of the equation 13x²+6√3xy+7y²=16, we can follow these steps:

1. Isolate the variables on one side of the equation. In this case, subtract 16 from both sides to get 13x²+6√3xy+7y²-16=0.
2. Observe the coefficients of the x², xy, and y² terms. They indicate the shape of the graph.
3. Based on the coefficients, determine the type of conic section represented by the equation. In this case, the coefficients suggest an ellipse.
4. Further analyze the coefficients to find the center, major and minor axes lengths, and orientation of the ellipse.
5. Plot the graph based on the information obtained.

Since the equation represents an ellipse, the graph will be a closed curve. The center, major and minor axes lengths, and orientation will determine the specific shape and position of the ellipse.