Answer :
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
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
