Question

Which conic's equation has 2 squares with the same signs and different leading coefficients?

Answer 1

We want to see which is the conic equation that has 2 squares with the same sign and different leading coefficients.

We will see that it is the equation of the ellipse.

Now let's see why that is the correct answer.

The general conic equation is of the form:

$A*(x - a)^2 + B*(x - b)^2 = R^2$

Where A and B are the leading coefficients, (a, b) is the center of the figure, and R is the average radius of the figure.

For example, if A = B, this would be the equation of a circle, but we must have two different leading coefficients.

If we write:

A = 1/C

B = 1/K

(both are positive, because "it has two squares with the same signs").

Then we get the equation:

$\frac{ (x - a)^2}{C} + \frac{(x - b)^2}{K} = R^2$

We get the equation we wanted.

The same sign in both square parts and different leading coefficients.

The above equation is the general equation of an ellipse.

If you want to learn more, you can read:

brainly.com/question/10311514