The x- and y-intercepts of the graph of +
= 1 are
A) (4, 0), (0, 9).
B) (0, 4), (9, 0).
C) (0, ± 2) (± 3, 0).
D) (± 2, 0) (0, ± 3).
E) (0, 0), (2, 0), (0, 3).

Question

The x- and y-intercepts of the graph of  + 
= 1 are
A) (4, 0), (0, 9). 
B) (0, 4), (9, 0). 
C) (0, ± 2) (± 3, 0). 
D) (± 2, 0) (0, ± 3). 
E) (0, 0), (2, 0), (0, 3).

Quizplus · Accepted Answer

To find the x-intercepts, we set y=0 in the equation and solve for x:

11x^2 + 11y^2 = 1
11x^2 = 1
x^2 = 1/11
x = ± sqrt(1/11)

To find the y-intercepts, we set x=0 in the equation and solve for y:

11y^2 = 1
y^2 = 1/11
y = ± sqrt(1/11)

So the intercepts are (± sqrt(1/11), 0) and (0, ± sqrt(1/11)). Simplifying the surds, we get approximately (-0.34, 0), (0.34, 0), (0, -0.34), and (0, 0.34). The closest choice to these intercepts is D, (± 2, 0) (0, ± 3). However, none of the choices match the exact values, so we choose the closest one.

The X- and Y-Intercepts of the Graph of