clasifying conics
4xsquared=64-64ysquared
4x^2 = 64 - 64y^2
4x^2 + 64y^2 = 64 .......divide each term by 64
(x^2)/16 + y^2 = 1
you should recognize the standard form of the equation of an ellipse.
To classify conics, we need to determine the shape of the curve represented by the given equation. In this case, the equation is 4x^2 = 64 - 64y^2.
First, we want to simplify the equation to a standard form. We can start by adding 64y^2 to both sides of the equation:
4x^2 + 64y^2 = 64
Next, we can divide each term by 64 to get:
(x^2)/16 + y^2 = 1
Now we have the equation in standard form. By comparing it with the general equation for conics, we can determine the shape of the curve.
The standard equation for an ellipse is (x^2/a^2) + (y^2/b^2) = 1, where a and b are positive constants.
Comparing our equation to the standard equation, we can see that a^2 = 16 and b^2 = 1.
Since a > b, we know that the major axis of the ellipse is the x-axis, and the minor axis is the y-axis. The shape of the curve is an ellipse.
Therefore, the given equation represents an ellipse.