Which of the following is an equation of the circle with its center at (0,0) that passes through (3,4) in the standard (x, y) coordinate plane?

Варианты ответов

x²+y²=25x-y=1x+y=25x²+y²=5

Answer: x² + y² = 25

Step-by-step explanation: As we have x²+y²=25 (A) as options,

x-y=1 (B)

x+y=25 (C)

x²+y²=5 (D)

We can rule out B and C as they are not circles. Circles must be

(x - xc) ² + (y - yc) ² = r². They must have index 2.

We have then A or D.

As the circle must pass through (3,4), we can substitute as x=3 and y=4

(A) 3² + 4² = 9 + 16 = 25 ok

(D) 3² + 4² = 9 + 16 = 25 ≠ 5

So, it is A, x² + y² = 25