Question

In Question 10 of Exploration 2.3.2 you were asked how to determine which conic section is generated given the general form 0=Ax^2+Cy^2+Dx+Ey+F (assume B=0 ). Which of the following is FALSE when determining a conic section from general form? If the conic section is a circle, then A=C. If the conic section is a circle, then A. C will be positive. If the conic section is an ellipse, then A and C will have the same sign. If the conic section is a hyperbola, then A⋅C will be positive. If the conic section is a parabola, then either A−0 or C=0.

Answer 1

When determining a conic section from the general form, different properties are considered for each type of conic section.

Step-by-step explanation:

When determining a conic section from the general form 0=Ax^2+Cy^2+Dx+Ey+F, there are several properties to consider:

1. If the conic section is a circle, then A=C and A and C will be positive.
2. If the conic section is an ellipse, then A and C will have the same sign. They can both be positive or both negative.
3. If the conic section is a hyperbola, then A⋅C will be negative. Their signs will be different.
4. If the conic section is a parabola, then either A≠0 or C=0
5. in the general form.

Answer 2

When determining a conic section from the general form, certain conditions apply depending on the type of conic section.

Step-by-step explanation:

When determining a conic section from the general form 0=Ax^2+Cy^2+Dx+Ey+F, the following statements are true:

1. If the conic section is a circle, then A=C.
2. If the conic section is a circle, then A and C will both be positive.
3. If the conic section is an ellipse, then A and C will have the same sign (both positive or both negative).
4. If the conic section is a hyperbola, then A*C will be negative.
5. If the conic section is a parabola, then either A=0 or C=0.