A circle has the equation 16x^2+16y^2=256. Hence sketch the curve 16x^2+16y^2=256
To sketch the curve represented by the equation 16x^2 + 16y^2 = 256, we can rewrite the equation in standard form for a circle: (x - h)^2 + (y - k)^2 = r^2.
First, let's divide the equation by 16 to simplify the equation:
x^2 + y^2 = 16
Comparing this equation to the standard form, we can see that h = 0, k = 0, and r^2 = 16. This indicates that the circle's center is at the origin (0, 0) and its radius is 4.
Since the equation doesn't involve any linear terms (x or y terms with degree 1), we can conclude that the circle is centered at the origin and has a radius of 4.
To sketch the curve, we can plot the origin as (0, 0) and draw a circle centered on the origin with a radius of 4.
The sketch of the curve looks like a circle centered at the origin with a radius of 4.