Identify all the required information from the equation given below. Then graph of the conic section -9x²+4y²-18x+16y=29
The required information from the equation is:
- Coefficients of x², y², x, and y terms: -9, 4, -18, 16
- Constant term: 29
To graph the conic section, we need to determine whether it is an ellipse, circle, hyperbola, or parabola. To do this, we can simply check the coefficients of x² and y²:
- If the coefficients of x² and y² are the same and have opposite signs, it is a hyperbola.
- If the coefficients of x² and y² are the same and have the same sign, it is a circle.
- If the coefficients of x² and y² are different, it is an ellipse.
In this case, the coefficients of x² and y² are not the same, so it is an ellipse. To graph the ellipse, we can first rewrite the equation in standard form by completing the square for x and y terms. Once in standard form, we can determine the center, major and minor axes, and then plot the ellipse accordingly.