Question

Which shape has a vertex of (-1, 5) and contains the point (3, -19)?

a) Circle
b) Parabola
c) Hyperbola
d) Ellipse

Answer 1

The shape that contains the point (3, -19) and has a vertex at (-1, 5) is an Ellipse.

Step-by-step explanation:

To determine which shape contains the point (3, -19) and has a vertex at (-1, 5), we can calculate the distance between the two points. The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the formula, substituting the values, we get:

d = √((3 - (-1))^2 + (-19 - 5)^2)

d = √(16^2 + (-24)^2)

d = √(256 + 576)

d = √(832)

d ≈ 28.84

Based on the given options, the shape that contains the point (3, -19) and has a vertex at (-1, 5) is the Ellipse because the distance between the two points is not constant, ruling out the circle, parabola, and hyperbola.