Generate Quiz 6A333060A03C0

The ratio of the length of the semi-major axis to the distance between the focus and the center is known as the eccentricity of a conic section.

The eccentricity values for the various conic sections are:

a) Parabola: Eccentricity = 1

Because a parabola has an eccentricity of 1, (a) Parabola is the right choice.

The right response is a

The given equation can be rewritten as follows:

2(x + y + 1) = 0.

Consequently, x + y + 1 = 0. Since the intersection of the x and y terms at zero is the center of a hyperbola, the center of this hyperbola is (-1, -1).

The response is (a) (-1,-1).

This is the right response. When u·(v×w), the triple scalar product of vectors u, v, and w, equals zero, the vectors are said to be coplanar. The three vectors are guaranteed to be in the same plane by this condition.

We can solve this system of linear equations to determine the intersection of the two lines, 5x + 7y = 35 and -7y + 3x = 21.

Let’s start by resolving the second equation, which is -7y + 3x = 21 for y:

-7y = -3x + 21

y = 3/7x – 3

In the first equation, 5x + 7y = 35, enter the expression for y from the second equation:

5x + 7(3/7x – 3) = 35

5x + 3x – 21 = 35

8x = 56

x = 7.

To find y, now enter x = 7 back into y = 3/7x – 3:

y = 3/7(7) – 3

y = 3 – 3.

y = 0.

Therefore, the point of intersection of the lines 5x + 7y = 35 and -7y + 3x = 21 is (7,0).

Since density only has a magnitude and no direction, it is a scalar quantity.