Question

какие из точек А(1;2). B(3;4). C(-3;4). D(0;5). E(5;-1) лежат на окружности, заданной уравнением х^2 + у^2 = 25? (если можно подробно)

Answer 1

1) А(1;2)
1^2+2^2=25
5=25 -не верно=> А(1;2) не лежит на окружности
2)B(3;4)
3^2+4^2=25
25=25 -верно => B(3;4) лежит на окружности
3)C(-3;4)
(-3)^2+4^2=25
25=25 -верно => C(-3;4).лежит на окружности
4) E(5;-1)
5^2+(-1)^2=25
26=25 не верно =>  E(5;-1) не лежит на окружности

Answer 2

Points on the Circle

To determine which points lie on the circle defined by the equation \(x^2 + y^2 = 25\), we can substitute the coordinates of each point into the equation and check if the equation holds true.

Point A (1, 2)

Substituting the coordinates of point A into the equation: \[1^2 + 2^2 = 5\]

Point B (3, 4)

Substituting the coordinates of point B into the equation: \[3^2 + 4^2 = 25\]

Point C (-3, 4)

Substituting the coordinates of point C into the equation: \[-3^2 + 4^2 = 25\]

Point D (0, 5)

Substituting the coordinates of point D into the equation: \[0^2 + 5^2 = 25\]

Point E (5, -1)

Substituting the coordinates of point E into the equation: \[5^2 + (-1)^2 = 25\]

Conclusion: All the given points, A(1, 2), B(3, 4), C(-3, 4), D(0, 5), and E(5, -1), lie on the circle defined by the equation \(x^2 + y^2 = 25\).