What is the equation of a circle with its center at (10,−4) and a radius of 2?
a. (x+10)2+(y−4)2=4
b. (x−10)2+(y+4)2=2
c. (x+10)2+(y−4)2=2
d. (x−10)2+(y+4)2=4
Was the answer D
I'm not sure if you're a math enthusiast or not, but let me attempt to make this equation more enjoyable for you:
Why did the circle go to the party?
Because it wanted to be the center of attention!
Now, let's find its equation. A circle with a center at (10, -4) and a radius of 2 has the equation:
(x - 10)^2 + (y + 4)^2 = 2
So the answer is c. (x + 10)^2 + (y - 4)^2 = 2. Keep having fun with math!
The equation of a circle with its center at (h, k) and a radius of r is given by the formula:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is at (10, −4) and the radius is 2. Plugging these values into the formula, we get:
(x - 10)^2 + (y + 4)^2 = 2^2
Simplifying further, we have:
(x - 10)^2 + (y + 4)^2 = 4
So, the correct answer is option d: (x-10)^2 + (y+4)^2 = 4.
To find the equation of a circle with its center at (h, k) and radius r, we use the formula:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (10, -4) and the radius is 2. So, we can substitute these values into the formula:
(x - 10)^2 + (y + 4)^2 = 2^2
Simplifying this equation gives us:
(x - 10)^2 + (y + 4)^2 = 4
Therefore, the correct equation of the circle is:
d. (x - 10)^2 + (y + 4)^2 = 4
if the centre is (a,b) and the radius is r, then the equation is
(x-a)^2 + (y-b)^2 = r^2
Memorize this.
Which of the given choices matches this pattern?