Question

Lauren describes a parabola where the focus has a positive, nonzero x-coordinate. Which parabola(s) could Lauren be describing? Check all that apply.

a) x^2 = 4y
b) y^2 = x
c) y^2 = 10x
d) x2 = –6y

Answer 1

Lauren could be describing parabolas given by options b) y^2 = x and c) y^2 = 10x, as these are equations of parabolas that open to the right, where the focus would have a positive, non-zero x-coordinate.

Step-by-step explanation:

Lauren is describing a parabola where the focus has a positive, nonzero x-coordinate. The equations that could represent such parabolas are those of the form y^2 = 4px (where p > 0, representing a parabola that opens to the right) or x^2 = 4py (where p < 0, representing a parabola that opens to the left). Analyzing the options given:

• Option a) x^2 = 4y: This parabola opens upward, not to the right or left, so the focus cannot have a positive x-coordinate.
• Option b) y^2 = x: This represents a parabola that opens to the right, so it could have a focus with a positive x-coordinate.
• Option c) y^2 = 10x: Similar to option b, this also represents a parabola that opens to the right, thus a focus with a positive x-coordinate is possible.
• Option d) x^2 = –6y: This parabola opens downward, so the focus would not have a positive x-coordinate.

Therefore, the parabola(s) Lauren could be describing are represented by options b and c.