True
False
False
That's false
Equation of any circle, with any radius, and its center at any point: [ x - (x-coordinate of the center) ]2 + [ y - (y-coordinate of the center) ]2 = (radius of the circle)2
True
True. The solution set of an equation of a circle consists of all the points that lie on the circle. This is defined by the standard equation of a circle, which is typically in the form ((x - h)^2 + (y - k)^2 = r^2), where ((h, k)) is the center and (r) is the radius. Any point ((x, y)) that satisfies this equation lies on the circle.
True. The solution set of an equation of a circle consists of all the points that lie on the circle itself. This set is defined by the equation ((x - h)^2 + (y - k)^2 = r^2), where ((h, k)) is the center and (r) is the radius. Thus, any point that satisfies this equation lies on the circle.
Substitute the values for the two variables in the second equation. If the resulting equation is true then the point satisfies the second equation and if not, it does not.
false
false
An ordered pair or coordinates of a point in 2-dimensional space.
To identify the center point of a circle from its equation, you typically look for the standard form of the circle's equation, which is ((x - h)^2 + (y - k)^2 = r^2). In this format, ((h, k)) represents the center of the circle, where (h) and (k) are constants. If you provide the specific equation of the circle, I can help you determine the center point.
7
False
False
To determine if the point (1, 1) satisfies the equation ( y = 6x ), we can substitute ( x = 1 ) into the equation. This gives us ( y = 6(1) = 6 ). Since the point has ( y = 1 ) but the equation gives ( y = 6 ), the point (1, 1) does not satisfy the equation.
It is a linear equation in two variables, x and y. Any point on the line defined by the equation will satisfy the equation and conversely, any ordered pair that satisfies the equation will represent a point, in the Cartesian plane, will be on the line.