Question

5 AB is the diameter of a circle whose center is the point (4,-3). If the coordinates of A are (-1,5), Find AB>

Answer 1

Given:

AB is the diameter of a circle whose center is the point (4,-3).

Coordinates of A are (-1,5).

To find:

The measure of AB.

Solution:

Let point O(4,-3) be the center of the circle.

Then, OA is the radius of the circle.

We know that, diameter of a circle is twice of its radius.

So, $AB=2(OA)$       ...(i)

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula, the distance between O and A is

$OA=\sqrt{(-1-4)^2+(5-(-3))^2}$

$OA=\sqrt{(-5)^2+(5+3)^2}$

$OA=\sqrt{25+(8)^2}$

$OA=\sqrt{25+64}$

$OA=\sqrt{89}$

Now, using (i), we get

$AB=2(OA)$

$AB=2(\sqrt{89})$

$AB=2\sqrt{89}$

Therefore, the measure of AB is $2\sqrt{89}$ units.