Question

How do you write the equation of a circle which has a center (7,3) and a diameter of 24?

Answer 1

In the above mentioned question we can easily see that the question has been asked to write the equation of a circle for which we require two things the center point and the diameter and both of them has been mentioned we will substitute it in the general equation of circle which will then give us are required equation of circle.

Complete step by step answer:
In the above question we are asked to find the general equation of the circle for which in the question itself they have given us the diameter of the circle and also the center of the circle. To proceed with the question we will first write the general equation of circle which is ${{\left( x-a \right)}^{2}}+{{\left( y-b \right)}^{2}}={{r}^{2}}$ in this equation r signifies the radius of the circle and “a'' and “b” signifies the x and y coordinates of the center of the circle. The values of “a'' and “b” has been mentioned in the question itself as we know the x and y coordinates of the center of the circle so we can substitute the value of “a” and “b” in the general equation of circle and we get: ${{\left( x-7 \right)}^{2}}+{{\left( y-3 \right)}^{2}}={{r}^{2}}$ now to get the radius in the question itself we know the diameter of the circle and we also know that diameter is twice of the radius of the circle so radius of circle will be half of diameter which we will get as 12 so radius of circle r = 12. Now we will substitute this in the equation of circle which we got form the general equation after substituting the x and y coordinates of the circle, so after substituting the radius of the circle we will get the equation of the required circle which is: ${{\left( x-7 \right)}^{2}}+{{\left( y-3 \right)}^{2}}={{12}^{2}}$

So the equation of the required circle is: ${{\left( x-7 \right)}^{2}}+{{\left( y-3 \right)}^{2}}={{12}^{2}}$

Note: In the above question that has been stated there is a general mistake that happens that is we generally forget to use the center of the circle the general equation of the circle is inclusive of the center of the circle, we ignore the center of the circle cause it is generally taken as zero but when it is mentioned we will have to substitute it in the equation.