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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.Equations of Circles - Equations of Circles Objective: To write an equation of a circle.
Ex. 1: Writing a Standard Equation of a Circle Write the standard equation of the circle with a | PowerPoint PPT presentation | free to view. - Elementary Arithmetic - High School Math - College Algebra - Trigonometry - Geometry - Calculus But let's start at the beginning and work our way up through the various areas of math.
We need a good foundation of each area to build upon for the next level. One-step equations are the simplest equations around. Why? Because they take only one step to solve. The main objective is to have only the variable (x or any other letter that is used) on one side and the numbers on the other side.
The number in front of the variable should be the number 1. A circle has an equation 49x^2+49y^2+14x+y=0 find the Center, Radius and intercepts of the circle. I need help solving this equation: 49x^2+49y^2+14x+y=0 find the Center, Radius and intercepts of the circle.
standard srmvision.coma.1 GEO/AII Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
The solution r = 0 just says that the graph should contain the pole, so the equation of the circle is: r = 2 a cos() Now plot some values of r and and check that you indeed get points on the circle .