Question

Write the equation of the circle with center (0, 0) and (5, 2) a point on the circle. A) x2 + y2 = 23 B) x2 + y2 = 25 C) x2 + y2 = 27 D) x2 + y2 = 29

Answer 1

the answer is D) x2 + y2 = 29

Answer 2

The equation of the circle is x² + y² = 29 ⇒ answer (D)

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)