If (x+2)^2+(y-5)^2=25 is the equation of a circle, which statement describes the circle's graph?
1 answer:
Answer:
B
Step-by-step explanation:
The standard form of a circle is
where h and k are the coordinates of the center of the circle and the radius is squared. The radius is easy...take the square root of 25 to get that the radius is 5. Since the pattern for the standard form is "x-" and "y-", if (x+2)^2 is the horizontal placement of the center, it actually was originally written as (x-(-2))^2, so the h coordinate is -2. Same goes for the vertical movement of the center. (y-(5))^2 means that the k coordinate is a positive 5.
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Sum/difference:
Let
This means that
Now, assume that is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that
was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.