Join IDNLearn.com to access a wealth of knowledge and get your questions answered by experts. Get accurate and detailed answers to your questions from our knowledgeable and dedicated community members.

Find the radius of the circle [tex]2x^2 + 2y^2 = 50[/tex].

A. [tex]\sqrt{50}[/tex]
B. 25
C. 50
D. 5


Sagot :

To find the radius of the circle given by the equation [tex]\(2x^2 + 2y^2 = 50\)[/tex], follow these steps:

1. Rewrite the Circle Equation:
The given equation of the circle is [tex]\(2x^2 + 2y^2 = 50\)[/tex].

2. Simplify the Equation:
Divide both sides of the equation by 2 to simplify it:
[tex]\[ \frac{2x^2 + 2y^2}{2} = \frac{50}{2} \][/tex]
This simplifies to:
[tex]\[ x^2 + y^2 = 25 \][/tex]

3. Identify the Standard Form:
The standard form of a circle's equation is [tex]\(x^2 + y^2 = r^2\)[/tex], where [tex]\(r\)[/tex] is the radius.

4. Compare with Standard Form:
Comparing [tex]\(x^2 + y^2 = 25\)[/tex] with [tex]\(x^2 + y^2 = r^2\)[/tex], we see that [tex]\(r^2 = 25\)[/tex].

5. Solve for the Radius:
To find the radius [tex]\(r\)[/tex], take the square root of both sides:
[tex]\[ r = \sqrt{25} \][/tex]
Therefore, we have:
[tex]\[ r = 5.0 \][/tex]

So the radius of the circle is [tex]\(5.0\)[/tex].

The correct answer is:
(D) 5