Answer:
The equation of the circle is x² + y² = 29 ⇒ answer (D)
Step-by-step explanation:
* Lets study the standard form of the equation of the circle
- If the circle has a center (h , k) , radius r and a general
point on it (x , y)
∴ The equation of the circle is (x - h)² + (y - k)² = r²
* In our problem the center of the circle is (0 , 0)
∴ The equation of the circle is (x - 0)² + (y - 0)² = r²
∴ The equation is x² + y² = r²
- (5 , 2) is a point on the circle, we can use it to find the radius
* Lets substitute the values of x and y in the equation of the circle
∵ x = 5 and y = 2
∴ (5)² + (2)² = r²
∴ r² = 25 + 4 = 29
∴ The equation of the circle is x² + y² = 29
* The answer is (D)
