Question

How do find the equation of the circle given centre (0, 0) and radius 7?

Answer 1

Hint: Here we have been given the centre and radius of the circle. There is only one way to solve this problem or rather obtain the equation of the circle from the given values that is to substitute all these values in the general equation of the circle. Substitute all the given information in the general equation and you get your desired equation.

Complete step by step solution:
We have been given here the centre of the circle and radius
We just have to substitute the value of the given information in the general equation of the circle.
The general equation of the circle is given by ${\left( {x - {\text{h}}} \right)^2} + {\left( {y - {\text{k}}} \right)^2} = {r^2}$
In this $r$is the radius and (h, k) represent the coordinates of the centre of the circle.
Now since we have been given that the centre is at origin that is (0, 0) we have the value of (h, k) as (0, 0) and the value of $r$ is given as 7
Now substituting all this given value in the general equation we get
$
 {\left( {x - {\text{h}}} \right)^2} + {\left( {y - {\text{k}}} \right)^2} = {r^2} \\
 \Rightarrow {\left( {x - 0} \right)^2} + {\left( {y - 0} \right)^2} = {7^2} \\
 \Rightarrow {x^2} + {y^2} = 49 \\
 $

Therefore ${x^2} + {y^2} = 49$ is the equation of the circle with centre (0, 0) and radius 7.

Note: Since in this case we have been given the centre of the circle as (0,0). But if in case the centre is other than (0,0) after substituting the values of the given information in the general equation you will have to solve the equation further so that it comes in the simplest form as this will be the final equation of the circle.