Geo QUESTIONS!!!?

Question

1. Find the center and the radius of the circle, (x+4)squared +(y+1)squared=100.
2. Write an equation of the circle that has center(1,5) and is tangent to the y-axis.
3. Find the midpoint of the segment with endpoints (a-2,b) and (a+4,b)

Answer 1

1)
General form of a circle is
(x - h)^2 + (y - k)^2 = r^2
where
r = radius
(h, k) is center.

so...
(x + 4)^2 + (y + 1)^2 = 100
could be written as
[x - (-4)]^2 + [y - (-1)]^2 = 10^2

from that, you should easily be able to see (h, k) and r.

2)
center is (1, 5).
tangent to y-axis means the radius is 5 units long. (Distance from the center to the y-axis.)

So, using the general formula I gave you in #1, you should be able to plug those numbers in.

3)
Midpoint is (average of x values, average of y values)

So...
average of x-values:
[(a - 2) + (a + 4)] / 2
= (2a + 2) / 2
= 2(a + 1) / 2
= a + 1

Average of y-values:
[b + b] / 2
= 2b / 2
= b

So, midpoint is (a + 1, b)

Answer 2

The radius is 10, the center is at (-4,-1)

The circle must have a radius of 1 for tangency with the y-axis. So the equation is (x-1)^2+(y-5)^2=1

If the y value for each end point is b, the segment must lie on an horizontal line. So the midpoint would be (a+1,b)