# How to find the point of a circle closest to the origin?

## Question:

How to find the point of a circle closest to the origin?

## Circle

The collection of all the points which are at equal distance from a fixed point is known as Circle. the fixed point is called the center of the circle and the fixed distance is called the radius of the circle. The standard equation of the circle is {eq}(x-h)^2+(y-k)^2=r^2 {/eq} Where (h,k) are the coordinates of the center of the circle and r is the radius of the circle.

## Answer and Explanation:

The standard equation of the circle is {eq}(x-h)^2+(y-k)^2=r^2 {/eq} Where (h,k) are the coordinates of the center of the circle and r is the radius of the circle.

To find the point on the circle which is closest to the origin, we can follow the following steps:

**Step1** Construct a distance function which is equal to the distance between the general point (x,y) on the circle and the point origin (0,0)

i.e. {eq}D=\sqrt{(x-0)^2+(y-0)^2} \\ =\sqrt{x^2+y^2} {/eq}

**Step2** Now make the distance function D of one variable i.e. use the equation of the circle to substitute the value of any variable in the equation of the distance function.

**Step3** Differentiate the distance function with respect to that independent variable and find the critical points.

**Step4**Use the first derivative test to find the extrema of the distance function.

**Step5** The point where the distance function will minimum will be the closest point to the origin.

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#### Learn more about this topic:

from Math 104: Calculus

Chapter 9 / Lesson 3