Ellipses Page 1

Page 1

Varying the Coefficients in the Equation
Ax² + By² = P to Find Ellipses

Remember that we can represent a circle centred at the origin in the following equivalent ways:
x² + y² = r², where |r| represents the radius.
Ax² + Ay² = P, where A and P must have the same sign.
Ax² + Ay² + F = 0, where A and F must have opposite signs.

Let's look at the form, Ax² + Ay² = P. What would happen if A continued to be the coefficient of x², but the coefficient of y² was changed to B, where B could be different than A?

Use the action figure below to explore what happens to the circle when A = 1, P = 1 and the value of B:
    1. increases
    2. is between 0 and 1
    3. equals 0
    4. is negative
Then use the action figure to explore what happens to the circle when B = 1, P = 1 and the value of A:
    1. increases
    2. is between 0 and 1
    3. equals 0
    4. is negative

Ax² + By² = P

Once you've explored these scenarios, use the questions on this side page to check your understanding of varying the values of A and B and the effect on the graph of the conic.