Could you please check some of my Algebra problems please?
Write the standard form of the equation of the circle with the given center and radius.
1. (-7,4);8
I got (x+7)^2 + (y-4)^2=64
2. (-7,10); square root of 17
I got (x+7)^2 + (y-10)^2=17
3. (0,0); 2 square root of 2
I got x^2+y^2=8
Find the center and the radius of the circle
7. (x-4)^2 + (y-1)^2=9
I got (4,1) as the center and the radius 3.
all correct.
Sure, I'd be happy to check your algebra problems. Let's go through each of the problems step by step to determine if your answers are correct.
1. (-7,4);8
To write the equation of a circle in standard form, you need the center coordinates (h, k) and the radius r. From the given information, we have the center at (-7, 4) and a radius of 8. The standard form equation of a circle is (x - h)^2 + (y - k)^2 = r^2. Plugging in the values, we get:
(x + 7)^2 + (y - 4)^2 = 8^2
(x + 7)^2 + (y - 4)^2 = 64
Your answer of (x + 7)^2 + (y - 4)^2 = 64 is correct.
2. (-7,10); square root of 17
Using the same process, we have the center at (-7, 10) and a radius of √17. Plugging in the values, we get:
(x + 7)^2 + (y - 10)^2 = (√17)^2
(x + 7)^2 + (y - 10)^2 = 17
Your answer of (x + 7)^2 + (y - 10)^2 = 17 is correct.
3. (0,0); 2 square root of 2
Again, we have the center at (0, 0) and a radius of 2√2. Plugging in the values, we get:
x^2 + y^2 = (2√2)^2
x^2 + y^2 = 8
Your answer of x^2 + y^2 = 8 is correct.
Now, let's move on to the center and radius of the given circle:
7. (x-4)^2 + (y-1)^2=9
By comparing this equation to the standard form equation of a circle, we can see that the center is (4, 1) and the radius is √9 = 3.
Your answer of (4, 1) as the center and a radius of 3 is correct.
Great job on solving these algebra problems!