For each pair of mathematical expressions, determine if the expressions have equal values. Select each pair of expressions that
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We have two points describing the diameter of a circumference, these are:
Recall that the equation for the standard form of a circle is:
Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.
For this we use the following equation:
Now, we replace and solve:
The center of the circle is (-8,-7), so:
On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation:
In this case, we will solve the delta with the center coordinate and the B coordinate.
Therefore, the equation for the standard form of a circle is:
In conclusion, the equation is the following:
#8
- y=4(x-0)²+0
Vertex at (0,0)
#11
- y=-6(x-0)²+0
Same Vertex
#14
- y=-(x-0)²+2
Vertex (0,2)
