Here’s a simulation that demonstrates the parametric equation of a circle. (x + g) 2 + (y + f) 2 = r 2 (where r 2 = g 2 + f 2 – c)Īgain, let P(x, y) be any point on the circle such that CP makes and angle θ with the X-axis.Īnd, this is the parametric equation of the circle x 2 + y 2 + 2gx + 2fy + c = 0. Complete the following for each equation in the table below: Write down the shifted equation (do not simplify). Parametric Equation for the General CircleĬonsider the general equation of the circle: Equation of a circle with centre at ((a b)) (EMCHV) Shifting the centre of a circle. We can also obtain the parametric equation of the circle whose center does not lie at the origin.
Or, any point on the circle is (rcosθ, rsinθ), where θ is a parameter. In other words, for all values of θ, the point (rcosθ, rsinθ) lies on the circle x 2 + y 2 = r 2. Here, θ is the parameter, which represents the angle made by OP with the X-axis.
where g, f, c are constants and center is (-g, -f) and radius r g 2 + f 2 c. General Equation of the Circle : The general equation of the circle is x 2 + y 2 + 2 g x + 2 f y + c 0. Using trigonometry, we’ll get:Īnd that’s it! We got what’s called the parametric equation of the circle. The general equation of the circle and standard form of circle are given below with examples. Let P(x, y) be any point on the circle such the OP makes an angle θ with the X-axis. Parametric Equation for the Standard CircleĬonsider the following circle, whose center is at O(0, 0) and radius equals r. Just like the parametric equation of a line, this form will help us to find the coordinates of any point on a circle by relating the coordinates with a ‘parameter’. This lesson will cover the parametric equation of a circle.
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