Question

What is the equation of a circle with center (5, 12) and solution

point (5,-1)?

Answer 1

`(x - 5)^(2)+(y-12)^(2) = 169`

Explanation:

The radius of the circle is computed with the help of the Pythagorean Theorem:

`r = \sqrt{(5-5)^(2)+[(-1)-12]^(2)}`

`r = 13`

The equation of the circle in standard form is:

`(x - 5)^(2)+(y-12)^(2) = 169`

Answer 2

(x - 5)^2 + (y - 12)^2 = 13.

Explanation:

Okay, one thing we must know is that a circle is a shape that has equal distance from a fixed point. Hence, in order to be able to write the equation of a circle, we will have to make use of the mathematical representation or equation below;

(x - h)^2 + (y - k)^2 = r^2. ------------------(1).

The equation (1) above is the standard Cartesian form for the equation of a circle.

Therefore, the centre is in the form of (h, k) = (5, 12) and the radius = r.

Also, point (x ,y) =(5,-1) is any point on the circle.

So, if we substitute the values in to thestandard Cartesian form for the equation in equation (1) above, we will have;

=> ( 5 - 5)^2 + (-1 - 12)^2 = r^2.

=> 0 + 169 = r^2.

r = √ (169).

r = 13.

Therefore, the equation of a circle with center (5, 12) and solution point (5,-1) is;

==> (x - 5)^2 + (y - 12)^2 = 13.