Math Doubts

Equation of a Circle when the circle touches the x-axis

An equation that represents a circle when the circle touches the $x$-axis at a point is called the equation of a circle touching the $x$-axis.

Introduction

The circle touches the horizontal axis at a particular point in a special case and it can be written mathematically in an equation.

circle touching the x axis

Let $C$ represents the centre of a circle and $P$ represents any point on its circumference. If the coordinates of the center are represented by $a$ and $b$, then the centre in coordinate form is written as $C (a, b)$.

Similarly, $P (x, y)$ represents a point on the circumference of the circle. In this case, the circle is touching the $x$-axis at a point and it can be expressed in a mathematical equation.

Simple form

$(x-a)^2+(y-b)^2 \,=\, b^2$

Expansion

$x^2+y^2\,-\,2ax\,\,–\,2by+a^2 \,=\, 0$

Alternative form

The above two equations are also written alternatively in the following two forms respectively if the coordinates of the center are represented by $h$ and $k$. It means, $C (h, k)$.

Simple form

$(x-h)^2+(y-k)^2 \,=\, k^2$

Expansion

$x^2+y^2\,-\,2hx\,\,–\,2ky+h^2 \,=\, 0$

Proof

Learn how to prove the equation of a circle when the circle touches the $x$ axis.

Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved