realism877 said:Homework Statement
6x2 + 8y2 + 32y - 16 = 0
Homework Equations
The Attempt at a Solution
I think I made a mistake.
This is how far I got
4(x-4)^+3(y+9)^=120
I made a mistake. Can someone delete this thread?
What did I do wrong?
A hyperbola is a type of conic section that has two distinct branches, while an ellipse is a closed curve with a single, continuous shape. In an ellipse, the distance from the center to any point on the curve remains constant, while in a hyperbola, the difference between the distances to the two foci remains constant.
The center of a hyperbola or ellipse is the point where the two axes intersect. To find the center, you can use the equation (h,k) which represents the coordinates of the center point on the x and y axes.
The standard form for the equation of a hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2 = 1 or (y-k)^2/a^2 - (x-h)^2/b^2 = 1, depending on the orientation of the hyperbola. The standard form for the equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1 or (y-k)^2/a^2 + (x-h)^2/b^2 = 1, depending on the orientation of the ellipse. Here, (h,k) represents the coordinates of the center point, and a and b represent the lengths of the semi-major and semi-minor axes respectively.
The foci of a hyperbola or an ellipse can be found using the equation c^2 = a^2 + b^2, where c is the distance from the center to the focus, and a and b are the lengths of the semi-major and semi-minor axes respectively. The foci are located on the major axis of the hyperbola or ellipse, with a distance of c from the center.
To find the equation for a hyperbola, you need to know the coordinates of the center point, the lengths of the semi-major and semi-minor axes, and the orientation of the hyperbola. To find the equation for an ellipse, you need to know the coordinates of the center point, the lengths of the semi-major and semi-minor axes, and the orientation of the ellipse. You may also need to know the coordinates of one or two points on the curve to determine the direction and magnitude of the axes.