All About Conics: Circles, Ellipses, Hyperbolas, and Parabolas
Conics are surprisingly easy! There are four types of conic sections, circles, parabolas, ellipses, and hyperbolas. The first type of conic, and easiest to spot and solve, is the circle. The standard form for the circle is (x-h)^2 + (y-k)^2 = r^2. The x-axis and y-axis radius are the same, which makes sense because it is a circle, and from
In order to graph an ellipse in standard form, the center is first plotted (the (h, k)). Then, the x-radius is plotted on both sides of the center, and the y-radius is plotted both up and down. Finally, you connect the dots in an oval shape. Finally, the foci can be calculated in an ellipse. The foci is found in the following formula, a^2 b^2 = c^2. A is the radius of the major axis and b is the radius of the minor axis. Once this is found, plot the points along the major axis starting from the center and counting c amount both directions.
In order to determine if an equation is an ellipse, the following three criteria must be met. There must be an x^2 and a y^2 just like in a circle. However, the coefficients of the x^2 and y^2 must be different. Finally, the signs must be the same. For example, equation 4 is an ellipse. 49x^2 + 25y^2 +294x 50y 759 = 0 has an x^2 and a y^2. It also has different coefficients in front of them, and finally, both have the same sign! There you have it, an ellipse!HyperbolasBoy, now it is starting to get tough! But dont worry, hyperbolas are not much more difficult than ellipses. Imagine two parabolas opposite each other either going up and down or left and right. There is a distance separating the vertices of both parabolas, and that is what a hyperbola looks like. The standard form for the hyperbola is either ((x-h)/(rx))^2 ((y-k)/(ry))^2 = 1 or ((y-k)/(ry))^2 ((x-h)/(rx))^2 = 1. Notice the change between a hyperbola and an ellipse is that the signs are different! If the negative sign is in front of the y, then the hyperbola will be horizontal, and if the negative sign is in front of the x,
In order to graph an ellipse in standard form, the center is first plotted (the (h, k)). Then, the x-radius is plotted on both sides of the center, and the y-radius is plotted both up and down. Finally, you connect the dots in an oval shape. Finally, the foci can be calculated in an ellipse. The foci is found in the following formula, a^2 b^2 = c^2. A is the radius of the major axis and b is the radius of the minor axis. Once this is found, plot the points along the major axis starting from the center and counting c amount both directions.
In order to determine if an equation is an ellipse, the following three criteria must be met. There must be an x^2 and a y^2 just like in a circle. However, the coefficients of the x^2 and y^2 must be different. Finally, the signs must be the same. For example, equation 4 is an ellipse. 49x^2 + 25y^2 +294x 50y 759 = 0 has an x^2 and a y^2. It also has different coefficients in front of them, and finally, both have the same sign! There you have it, an ellipse!HyperbolasBoy, now it is starting to get tough! But dont worry, hyperbolas are not much more difficult than ellipses. Imagine two parabolas opposite each other either going up and down or left and right. There is a distance separating the vertices of both parabolas, and that is what a hyperbola looks like. The standard form for the hyperbola is either ((x-h)/(rx))^2 ((y-k)/(ry))^2 = 1 or ((y-k)/(ry))^2 ((x-h)/(rx))^2 = 1. Notice the change between a hyperbola and an ellipse is that the signs are different! If the negative sign is in front of the y, then the hyperbola will be horizontal, and if the negative sign is in front of the x,
Bibliography: eisstein, Eric W. "Conic Section." From MathWorld--A Wolfram Web Resource. .