MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

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)