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Harlamova29_29 [7]
3 years ago
10

What is a radius of a circle given by the equation x²-2x+8y-47=0

Mathematics
2 answers:
Zolol [24]3 years ago
7 0
First, we are going to rewrite it as a parabola equation.
Rewrite.
8y=-x^2+2x+47
Divide by 8.
y=-\frac{x^2}{8}+\frac{x}{4}+\frac{47}{8}
Factor out coefficient.
y=-\frac{1}{8}\left(x^2-2x\right)+\frac{47}{8}
Then, we are going to convert x into square form.
y=-\frac{1}{8}\left(x^2-2x+1\right)+\frac{1}{8}\cdot \:1+\frac{47}{8}
Convert the whole expression into square form.
y=-\frac{1}{8}\left(x-1\right)^2+\frac{1}{8}\cdot \:1+\frac{47}{8}
Simplify.
y=-\frac{1}{8}\left(x-1\right)^2+6
Subtract 6 from both sides.
y-6=-\frac{1}{8}\left(x-1\right)^2
Divide by coefficient.
-8\left(y-6\right)=\left(x-1\right)^2
Rewrite in standard form.
4\left(-2\right)\left(y-6\right)=\left(x-1\right)^2

The radius of the circle will be -2. Also, no matter what the sign says, the radius has to always be positive. 
Have a nice day! :)
fomenos3 years ago
5 0

Answer: the radius is 8 units

Step-by-step explanation:

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