SOLUTION: I'm so lost on this equation: Find the equation of the circle centered at (4,6) passing (2,2). Thank you for the person that is willing to help!

Question 530394: I'm so lost on this equation:
Find the equation of the circle centered at (4,6) passing (2,2).
Thank you for the person that is willing to help!
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
The standard form of the equation for a circle is:
...
(x - h)^2 + (y + k)^2 = r^2
...
Where h = the x coordinate of the center of the circle
Where k = the y coordinate of the center of the circle
Where r = the radius of the circle
...
We are given the center of the circle: (4, 6)
We are given one of the points the circle passes through: (2, 2)
...
The only thing we are missing to complete the equation for the circle is to know (if given) or derive (if not given), r, the radius of the circle.
...
With the two points given: center = 4, 6 and circle passes through 2, 2; if we connect those two points together, that line = the radius of the circle.
...
To determine the radius, think about a right triangle that has as its "a" side and "b" side the rise and run difference between the two given points. And, knowing the Pythagorean theorem to determine the hypotenuse of a right triangle:
...
a^2 + b^2 = c^2
...
We know that in in this instance the hypotenuse = the radius of our circle, so we will substitute r for c. If we take the square root of both sides of the previous equation we get:
...
r = SQRT(a^2 + b^2)
...
To solve:
...
a = the difference in the two x coordinates (from the two points given):
a = 4 - 2 = 2
...
b = the difference in the two y coordinates (from the two points given):
b = 6 - 2 = 4
...
r = Sqrt(2^2 + 4^2)
r = Sqrt(4 + 16)
r = Sqrt(20)
...
To return to the original problem: determine the equation for the circle with the given center point and passing through the given point:
...
(x - 4)^2 + (y + 6)^2 = Sqrt(20)^2
...
which could be simplified to:
(x - 4)^2 + (y + 6)^2 = 20
...
cheers,
Lee
RELATED QUESTIONS
find an equation of the circle centered at (6,-5) and passing through (1,7) thank... (answered by stanbon)

Find the equation of the circle centered at (4,6) and passing through the point (2,2). (answered by jim_thompson5910,stanbon)

how i do this? find the equation of a circle centered at the origin, and having radius (answered by AnlytcPhil)

I am completely lost on this problem can you please explain? A sales person observes... (answered by marcsam823)

Write the equation in standard form for the circle passing through(0,7/2)centered at the... (answered by richwmiller)

find the equation of the circle centered at (3,-9) and passing throught point... (answered by solver91311)

Hello! You are all wonderful and have been such a big help to me! Thank you so much for... (answered by sophxmai,Alan3354)

Question provided by co-worker I'm trying to help... Given the equation x^2 + 6sqrt2x (answered by stanbon)

Which is the equation of a circle that passes through (2.2) and is centered at (5.6)... (answered by Alan3354,MathLover1,MathTherapy)