How do you identity if the equation #4x^2+2y^2=8# is a parabola, circle, ellipse, or hyperbola and how do you graph it?
The reference for Conic Section - General Cartesian form tells you how to determine what conic section it is.
The reference for Conic Section - General Cartesian form tells you how to determine what conic section it is, when given the General Cartesian form:
Here is the given equation in the general form:
Please observe the value of
Divide both sides of the original equation by 8:
Write the denominators as squares:
Insert zeros within the squares in the numerators:
This is the standard form for an ellipse, because it is easy to see:
- The center is (0, 0)
#y = 0, x = -2 and 2#
#x = 0, y = -sqrt(2) and sqrt(2)#
You may use these four points to graph the equation:
And then sketch in an ellipse around the center.
Here is a graph of the equation: