Find the equation of the circle that passes through the origin and x-intercept 1 and y-intercept 0. (standard form again)
goes through (0,0) and (1,0) (0,0) ??
woah, oops. the y-intercept is 2.
To find the equation of a circle, we need to know the coordinates of its center and its radius.
Given that the circle passes through the origin, we know that the center of the circle is at (0, 0).
To find the radius of the circle, we can use the distance formula between the center of the circle and one of the intercepts. Let's use the x-intercept (1, 0):
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Plugging in the values, our distance formula becomes:
Distance = √((1 - 0)² + (0 - 0)²) = √(1) = 1
Therefore, the radius of the circle is 1.
Now that we know the center (0, 0) and the radius (1), we can write the equation of the circle in the standard form:
(x - h)² + (y - k)² = r²
Where (h, k) represents the center of the circle, and r represents the radius.
Plugging in the values, our equation becomes:
(x - 0)² + (y - 0)² = 1²
Simplifying further:
x² + y² = 1
Thus, the equation of the circle that passes through the origin and has an x-intercept of 1 and a y-intercept of 0 is x² + y² = 1 in standard form.