Find the x- and y-intercepts of the graph of the equation. (If an answer does not exist, enter DNE.) y2 = 4 − x2

Question

Find the x- and y-intercepts of the graph of the equation. (If an answer does not exist, enter DNE.)

y² = 4 − x²

x-intercepts	(x, y) =					(smaller x-value)	(x, y) =
(larger x-value)
y-intercepts
(x, y) =
(smaller y-value)
(x, y) =
(larger y-value)

Answer 1

the equation is a circle with radius 2 and center at the origin (0,0)

x^2 + y^2 = 2^2

it has x intercepts at x=2 and x =-2 or the points (2,0) and (-2,0)

its y intercepts are y=2 and y =-2 or the points (0,2) and (0,-2)

just take the radius length and add and subtract it from the origin's x and y coordinates.

Answer 2

You are asked to find the x- and y-intercepts of the equation y² = 4 - x².

You can rewrite this equation as x² + y² = 4.

To find the x-intercept, you set the y variable equal to 0 and solve for x.

When y = 0, the equation becomes:

x² +0² = 4

x² = 4

Take the square root of both sides

x = 2, -2

So, for this equation, your x-intercepts occur at x = 2 and x = -2, and are (-2,0) and (2,0).

Similarly, to find the y-intercept , you set the x variable equal to 0 and solve for y.

When x = 0, the equation becomes:

0^{2 +} y² = 4

y² = 4

y = 2, -2

So, for this equation, the y-intercepts occur at y = -2 and y = 2, and are (-2,0) and (2,0).