Graph funtion, state asymptotes, foci, directrix, where applicable.

Question

x^2+ y^2=25.

Answer 1

The equation is x^2+ y^2=25.

The above equation represent the circle equation.

The standard form of circle equation with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.

Write the above equation in the standard form of circle.

(x - 0)^2+ (y - 0)^2 = 5^2

Center = (h, k) = (0, 0) and r = 5.

The circle has no directrix, or asymptotes or foci.

Draw coordinate plane.

Plot center (0, 0) and draw a circle with radius 5 from the point (0, 0).

Answer 2

The function is x ² + y ² = 25.

Standard form of a circle equation is (x - h )² + (y - k )² = r ², where center is (h ,k ) and radius of circle is r .

The given equation represents the circle equation.

The circle has no directrix, or asymptotes or foci.

Write the given equation in the standard form of a circle equation.

(x - 0)² + (y - 0)² = 5².

Compare it to standard form of a circle equation : (x - h )² + (y - k )² = r ².

Center (h, k ) = (0, 0) and radius (r ) = 5.

Graph the circle :

Center at (0, 0) and r = 5,So we plot

Up (0, 0 + 5) = (0, 5)

Down (0, 0 - 5) = (0, - 5)

Left (0 - 5, 0) = (-5, 0)

Right (0 + 5, 0) = (5, 0).

1. draw the coordinate plane.

2. Plot the center at (0, 0).

3. Plot 4 points " radius away from the center in the up, down, left and right direction.

4. Connect the plotted points to the graph of the circle with a round, smooth  curve.