Equation of Circle Touching Y -axis
We can easily find the equation of a circle touching the y-axis. Suppose the circumference of the circle touches the y-axis at point (0, b) and (r, b) is the centre of the circle with radius r.
We know that if a circle touches the y-axis, then its x-coordinate of the centre of the circle is equal to the radius r, this condition is shown in the image below,
Take any general point (x, y) on the circumference of the circle then its equation is given as,
Distance between (x, y) and (r, b) = Radius(r)
√[(x -r)2 + (y-b)2] = r
Squaring both sides we get,
(x -r)2 + (y-b)2 = r2
This is the equation of the circle touching the y-axis.
Equation of a Circle
Equation of a circle is the algebraic way to define a circle. It is the locus of the point which is at a constant distance from a fixed point. The fixed point is called the center of the circle, and the constant distance is called the radius of the circle. The equation of a circle is very useful for finding different parameters such as the circumference, and area of the circle.
A circle in 2-D and the 3-D planes is represented using the equation of the circle. It is the algebraic equation solution which represents all the points on the circumference of the circle. We can represent the equation of the circle in various forms, some of the common forms of the equation of the circle are,
- General form
- Standard form
- Parametric form
- Polar form
In this article, let’s learn about the equation of the circle, various forms of circle, and how to find the equation of the circle etc.
Table of Content
- What is the Equation of a Circle?
- Different Forms of Equation of Circle
- General Equation of a Circle
- Features of General Equation of Circle
- Equation of a Circle in Standard Form
- Parametric Equation of a Circle
- Equation of a Circle in Polar Form
- Equation of a Circle Formula
- Derivation of Circle Equation
- Graphing Equation of Circle
- How to Find Equation of Circle?
- Equation of Circle when Center at (x1, y1)
- Equation of Circle With Center at the Origin
- Equation of Circle with Centre on x-axis
- Equation of Circle with Centre on y-axis
- Equation of Circle Touching x-axis
- Equation of Circle Touching Y -axis
- Equation of Circle Touching Both X and Y Axes
- Converting General Form of Circle Equation to Standard Form
- Converting Standard Form of Circle Equation to General Form
- Features of Equation of Circle
- Practice Problems on Equation of a Circle
- Practice Problems on Equation of a Circle