Write the equation in standard form of the circle with the given properties.
Center at the origin; r = square root of 2
answer r= square root 2
or is this the correct answer x^2+y^2=2
oddly enough, both answers are correct!
in rectangular coordinates, x^2+y^2 = 2
in polar coordinates, r=√2
(but something tells me you have not yet studied polar coordinates -- you'll like them.)
To write the equation in standard form of a circle with the given properties: center at the origin and radius equals square root of 2, we use the equation:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the center coordinates and r is the radius. Since the center is at the origin, (h, k) = (0, 0). Substituting these values into the equation, we get:
(x - 0)^2 + (y - 0)^2 = (square root of 2)^2
Simplifying further,
x^2 + y^2 = 2
Therefore, the equation in standard form of the circle is x^2 + y^2 = 2.
To express the equation of a circle in standard form, we use the general equation for a circle:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) represents the coordinates of the center of the circle, and r represents the radius.
In this case, the center is given to be at the origin (0,0), and the radius is equal to the square root of 2.
Substitute these values into the equation:
(x - 0)^2 + (y - 0)^2 = (square root of 2)^2
This simplifies to:
x^2 + y^2 = 2
So, the equation of the circle in standard form with a center at the origin and a radius of the square root of 2 is:
x^2 + y^2 = 2