Answer:
(x - 5)^2 + (y - 12)^2 = 13.
Step-by-step 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.
Answer:
[tex](x - 5)^{2}+(y-12)^{2} = 169[/tex]
Step-by-step explanation:
The radius of the circle is computed with the help of the Pythagorean Theorem:
[tex]r = \sqrt{(5-5)^{2}+[(-1)-12]^{2}}[/tex]
[tex]r = 13[/tex]
The equation of the circle in standard form is:
[tex](x - 5)^{2}+(y-12)^{2} = 169[/tex]
