Math Doubts

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

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

Introduction

A circle touches the vertical axis at a point in a special case and it can be expressed mathematically in a mathematical equation.

circle touching the y-axis

Let $C$ be a center (or centre) be a point on the circumference of a circle. The centre $C$ with its coordinates is written as $C(a, b)$ in mathematical form if the horizontal and vertical distances of the centre $C$ are $a$ and $b$ units from the origin.

Let us assume that a point on the circumference of circle is denoted by $P$. The point $P$ in coordinate form is written as $P(x, y)$ mathematically if the horizontal and vertical distances of the point $P$ are $x$ and $y$ units from the origin.

Simple form

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

Expansion

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

Alternative form

If the coordinates of the center (or centre) are denoted by $h$ and $k$, then the centre in coordinate form is written as $C(h, k)$. Therefore, the above circle’s equations are written as follows.

Simple form

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

Expansion

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

Proof

Learn how to derive the equation of a circle when the circle is touching the $y$-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