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The equation of a circle with center the origin **(0,0)**, and radius ** r**, is:

This equation comes from the __ Distance Formula__.

The distance of the radius, which is a straight line, from the central point

=>

Find the equation of the circle with center **(0,0)**, passing through **(4,-2)**.

(4,-2)

Equation of circle is

Is the point

inside, on the edge, or outside the circle with equation

The circle equation tells us radius distance to the edge of the circle is

Now to consider the point

Using the

Telling us that the distance from point **(3,4)** to center **(0,0)** is **5**.

A distance of size

So the point **(3,4)**  is inside the circle.

The situation is illustrated below.

and Radius r

When the center of a circle isn’t the origin **(0,0)**, the equation is slightly different.

Like before, making use of the distance formula.

The equation is

A circle has equation

What are the values of the center and radius of the circle?

From the equation:

The radius is **√49** = **7**.

What is the equation of a circle with center

center

Now making use of the coordinates of point A, and inputting them into the equation.

A

Radius =

Equation of the circle is

Find the equation of a circle which has points E

The diameter is a straight line from one side of a circle to the other side.

It also passes through the center, which is in the middle of the line.

So the center of the circle **C** is the mid-point of the diameter from one edge to the other,
here from **E** to **F**.

Center

To find the value of the length of the radius, we can use either of the original end points given in the question.

Here we'll use F

Complete Equation of circle is:

A circle has center **C** (-**2**,-**3**).

Point **D** (**6**,**1**) lies on the edge of the circle.

What is the equation of the tangent at **D**?

A Tangent line to a circle, is a line that touches 1 point on the edge of the circle.

It is a straight line perpendicular to the radius line coming from the center point.

Gradient of radius from **C** to **D**:

m

For perpendicular lines, when gradients are multiplied together, m1 × m2 = -

So the gradient of the tangent at

Now we have enough information to form the tangent line equation.

 a  b

(

If the point **(n,4)**  lies on the edge
of the circle with equation **( x** −

What are the two possible values of

(n,4)

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