$x^2 + y^2 = r^2$

Consider a circle in two dimensional space and centre of the circle coincides with the origin of the two dimensional Cartesian coordinate system. It is assumed that the radius of the circle is $r$. Consider a point $P$ on the circumference of the circle and its coordinates are $x$ and $y$. Therefore, the point is $P (x, y)$.

Connect centre of the circle with point $P$ by a line. Draw a line from point $P$ and it should be parallel to $y$-axis and perpendicular to $x$-axis. The drawn line intersects the $x$-axis at point $Q$. The geometric process formed a right angled triangle $PCQ$.

As per right angled triangle $PCQ$

- Length of the opposite side is $PQ = y$
- Length of the adjacent side is $CQ = x$
- Length of the hypotenuse $CP = r$

According to Pythagorean Theorem, the sides of $\Delta PCQ$ is expressed as follows.

${CP}^2 = {CQ}^2 + {PQ}^2$

$\implies r^2 = x^2 + y^2$

$\therefore \,\,\,\,\, x^2 + y^2 = r^2$

It is a circle’s equation in algebraic form when the centre of the circle coincides with the origin of the coordinate system.

List of most recently solved mathematics problems.

June 18, 2018

Algebra Trigonometry

Find $x^3+\dfrac{1}{x^3}$ if value of $x+\dfrac{1}{x}$ equals to $2\cos{θ}$

Jun 13, 2018

Limit

Learn how to solve Limit of (1-cos6x)/(1-cos7x) as $x$ approaches $0$

Jun 09, 2018

Trigonometry

Find ΣtanAtanB, if A+B+C = 90°

May 30, 2018

Trigonometry

Find cos 40° + cos 80° + cos 160°

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.