Site Navigation Conic Sections: Hyperbolas In this lesson you will learn how to write equations of hyperbolas and graphs of hyperbolas will be compared to their equations. A hyperbola is all points found by keeping the difference of the distances from two points each of which is called a focus of the hyperbola constant.

Expanded equation of a circle Video transcript - [Voiceover] So we have a circle here and they specified some points for us. This little orangeish, or, I guess, maroonish-red point right over here is the center of the circle, and then this blue point is a point that happens to sit on the circle.

And so with that information, I want you to pause the video and see if you can figure out the equation for this circle.

Alright, let's work through this together. So let's first think about the center of the circle. And the center of the circle is just going to be the coordinates of that point.

So, the x-coordinate is negative one and then the y-coordinate is one.

So center is negative one comma one. And now, let's think about what the radius of the circle is. Well, the radius is going to be the distance between the center and any point on the circle.

So, for example, for example, this distance. The distance of that line. Let's see I can do it thicker. A thicker version of that. This line, right over there. Something strange about my Something strange about my pen tool.

It's making that very thin. Let me do it one more time. So how can we figure that out? Well, we can set up a right triangle and essentially use the distance formula which comes from the Pythagorean Theorem. To figure out the length of that line, so this is the radius, we could figure out a change in x.

So, if we look at our change in x right over here. Our change in x as we go from the center to this point. So this is our change in x. And then we could say that this is our change in y. That right over there is our change in y. And so our change in x-squared plus our change in y-squared is going to be our radius squared.

That comes straight out of the Pythagorean Theorem. This is a right triangle. And so we can say that r-squared is going to be equal to our change in x-squared plus our change in y-squared.

Plus our change in y-squared. Now, what is our change in x-squared? Or, what is our change in x going to be?Writing Equations in Standard Form.

We know that equations can be written in slope intercept form or standard form. Ax +By= C We can pretty easily translate an equation from slope intercept form into standard form.

Let's look at an example. Example 1: Rewriting Equations in Standard Form. Rewrite y = 2x - 6 in standard form. (ellipse)Reduce the equation 32𝑥2 + 50𝑦2 − 𝑥 − = 0 to standard form.

Reduce the equation 32𝑥2 + 50𝑦2 − 𝑥 − = 0 to standard form. Locate the center, foci, vertices, ends of latera recta, and trace the curve.

Standard Form Equation of an Ellipse. The general form for the standard form equation of an ellipse is. Horizontal Major Axis Example. Example of the graph and equation of an ellipse on the Cartesian plane: The major axis of this ellipse is horizontal and is the red segment from (-2,0) to (2,0).

For each ellipse, determine the vertices, co-vertices, center and foci. 50x2 + 2y2 = 50 61)) {£10) s' Given the center and the radius, write the equation for the circle in standard form.

-? co, Write each circle in standard form and graph each.

0) For each circle, determine the center of the circle: the radius and then graph each. SOLUTION: Use the information provided to write the standard form of the ellipse: Vertices: (-9,3),(-9,) Foci: (-9,2), (-9,) Please provide a step by step answer. Improve your math knowledge with free questions in "Convert equations of ellipses from general to standard form" and thousands of other math skills.

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