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SmokeyRN
18.05.2021 •
Mathematics
1.This circle is centered at the origin and contains the points two units away. Write the equation for this circle.
The equation for this circle is x2+y2= ______
2.Show that the two points shown on the circle are solutions to your equation.
I can show that 1, 3 is a solution to this equation by showing that it makes the equation true: 12+32= 1 + 3 = ______ = 22 .
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Ответ:
1. The location of the center of the given circle = The origin (0, 0)
The given points on the circumference of the circle = (1, √3), and (0, -2)
The general form of the equation of a circle, is presented as follows
(x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The radius of the circle
∴ (h, k) = (0, 0)
The radius of the given equation is the distance from the center (0, 0) to either the point (0, -2) or (1, √3)
The distance from the center (0, 0) to the point (0, -2), which are points on the same ordinate, r = y₂ - y₁
∴ r = 0 - (-2) = 2
r = 2
The equation of the circle is therefore;
(x - 0)² + (y - 0)² = 2²
∴ x² + y² = 2²
2. When x = 1, and y = √3, we have;
(1 - 0)² + (√3 - 0)² = 1 + 3 = 4 = 2²
When x = 0, and y = -2, we have;
(0 - 0)² + ((-2) - 0)² = (-2)² = 4 = 2²
Therefore, the points shown on the circle (1, √3), and (0, -2) satisfy the equation of the circle, x² + y² = 2² and are solutions to the equation of the circle
Step-by-step explanation:
Ответ:
mind if I get free points.
Step-by-step explanation: