Quiz about PRE-LIM (STEM 4A

Question 1

It is formed when the plane intersects the cone or the double-napped cone to create a figure.

Accepted Answer

Conic Section.

Answer

<a target="_blank" rel="noopener noreferrer nofollow" style="text-decoration: underline; cursor: pointer;" href="http://A.Circle">Circle</a>

Answer

Parabola

Answer

Hyperbola

Question 2

The following are the degenerate conics section:

Accepted Answer

Line, Point, Intersecting lines

Answer

Hyperbola, Parabola, Ellipse, Circle

Answer

Conic section, Hyperbola, Parabola, Ellipse,

Answer

Circle, Single Line, Point, Parabola

Question 3

Write an equation of a circle that lies on the origin and the length of its radius is 1.

Accepted Answer

$$x^2+y^2=1$$

Answer

$$\left(x-1\right)^2+\left(y-1\right)^2=1$$

Answer

$$x^2+y^2=2$$

Answer

$$\left(x-1\right)^2+\left(y-1\right)^2=2$$

Question 4

1. Determine the center and the length of the radius of the circle described in the equation $$\left(x+5\right)^2+\left(y-2\right)^2=16$$

Accepted Answer

center: (-5, 2)

radius: 4

Answer

center: (5,-2)

radius: 16

Answer

center: (-5, -2)

radius: $$4^2$$

Answer

center: (5, 2)

radius: $$16^2$$

Question 5

Given the equation of a circle $$\left(x+1\right)^2+\left(y-3\right)^2=16$$ , identify the general form of the circle.

Accepted Answer

$$x^2+y^2+2x-6y-6=0$$

Answer

$$x^2+y^2-2x+6y-26=0$$

Answer

$$x^2+y^2+2x-6y+6=0$$

Answer

$$x^2+y^2+2x+6y+26=0$$

Question 6

Convert the equation of $$x^2+4x+y^2-18y=15$$ , into standard equation of a Circle.

Accepted Answer

$$\left(x+2\right)^2+\left(y-9\right)^2=100$$

Answer

$$\left(x-2\right)^2+\left(y+9\right)^2=100$$

Answer

$$\left(x+2\right)^2+\left(y-9\right)^2=10$$

Answer

$$\left(x-2\right)^2+\left(y+9\right)^2=10$$

Question 7

The center of the circle is at C(-6, -5 ). If the radius is 8, what is the standard equation of the circle?

Accepted Answer

$$\left(x+6\right)^2+\left(y+5\right)^2=64$$

Answer

$$\left(x-6\right)^2+\left(y-5\right)^2=8$$

Answer

$$\left(x+6\right)^2+\left(y+5\right)^2=8$$

Answer

$$\left(x-6\right)^2+\left(y-5\right)^2=64$$

Question 8

If we have an equation of a parabola $$\left(x+7\right)^2=24y$$ , identify the length of the latus rectum.

Accepted Answer

24

Answer

0

Answer

6

Answer

7

Question 9

If we have the $$\left(y+6\right)^2=16\left(x-1\right),$$ identify the coordinates of vertex.

Accepted Answer

(1, -6)

Answer

(6, 1)

Answer

(6, -1)

Answer

(-6, -1)

Question 10

Given the standard equation of a parabola $$\left(x+3\right)^2=16\ \left(y-2\right),$$ identify the focal distance (p).

Accepted Answer

4

Answer

2

Answer

3

Answer

16

Question 11

Identify the center of an ellipse given the equation $$\frac{\left(x-10\right)^2}{36}+\frac{\left(y-9\right)^2}{84}=1\ .$$

Accepted Answer

center: (10, 9)

Answer

center: (-10, 9)

Answer

center: (10, -9)

Answer

center: (-10, -9)

Question 12

Given the equation of an ellipse $$\frac{x^2}{25}+\frac{y^2}{64}=1$$ , identify the value of 'c' .

Accepted Answer

$$\sqrt[]{39}$$

Answer

$$39$$

Answer

$$-39$$

Answer

- $$\sqrt[]{39}$$

Question 13

Write the standard equation of an ellipse given the coordinates of the foci (1, - 4) and ( -7 , - 4) and the major axis is 16 units.

Accepted Answer

$$\frac{\left(x+3\right)^2}{64}+\frac{\left(y+4\right)^2}{48}=1$$

Answer

$$\frac{\left(x+3\right)^2}{64}+\frac{\left(y-4\right)^2}{48}=1$$

Answer

$$\frac{\left(x-3\right)^2}{48}+\frac{\left(y-4\right)^2}{64}=1$$

Answer

$$\frac{\left(x+4\right)^2}{48}+\frac{\left(y-3\right)^2}{64}=1$$

Question 14

Find the endpoints of major axis of an ellipse given by an equation of $$\frac{\left(x+5\right)^2}{49}+\frac{\left(y-2\right)^2}{64}=1.$$ .

Accepted Answer

$$V_1:\ \left(-5,\ \ 10\right),$$ $$V_2:\ \left(-5,\ -6\right)$$

Answer

$$V_1:\ \left(-5,\ -10\right),\ \ $$ $$V_2:\ \left(5,\ 6\right)$$

Answer

$$W_1:\ \left(-2,\ 5\right)$$ $$W_2:\ \left(-5,\ 2\right)$$

Answer

$$W_1:\ \left(-5,\ -2\right)$$ $$W_2:\ \left(5,\ 2\right)$$

Question 15

Identify the length of major and minor axis of an ellipse given the equation $$\frac{\left(x+2\right)^2}{81}+\frac{\left(y-5\right)^2}{16}=1.$$

Accepted Answer

Major axis: 18 units

Minor axis: 8 units

Answer

Major axis: 5 units

Minor axis: 2 units

Answer

Major axis: 81 units

Minor axis: 16 units

Answer

Major axis: 9 units

Minor axis: 4 units

Question 16

If we have an equation of ellipse $$\frac{x^2}{36}+\frac{\left(y-4\right)^2}{25}=1,$$ identify the value of a.

Accepted Answer

a = 6

Answer

a = 5

Answer

a = -6

Answer

a = -5

Question 17

If we have an equation of ellipse $$\frac{x^2}{36}+\frac{\left(y-4\right)^2}{25}=1,$$ identify the value of b.

Accepted Answer

b = 5

Answer

b = 6

Answer

b = -6

Answer

b = -5

Question 18

If we have an equation of ellipse $$\frac{x^2}{36}+\frac{\left(y-4\right)^2}{25}=1,$$ identify the value of c.

Accepted Answer

c = $$\sqrt[]{11}$$

Answer

c = $$11$$

Answer

c = $$-11$$

Answer

c = $$-\ \sqrt[]{11}$$

Question 19

If we have an equation of ellipse $$\frac{x^2}{36}+\frac{\left(y-4\right)^2}{25}=1,$$ identify the coordinates of center.

Accepted Answer

center : (0, 4)

Answer

center : (0, -4)

Answer

center : (-4, 0)

Answer

center : (4, 0)

Question 20

The major axis and minor axis always have the same length.

Accepted Answer

False

Answer

True

Question 21

The endpoints of a major axis of an ellipse are the co-vertices.

Accepted Answer

False

Answer

True

Question 22

The endpoints of a minor axis of an ellipse are the vertices.

Accepted Answer

False

Answer

True

Question 23

The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.

Accepted Answer

True

Answer

False

Question 24

The midpoint of an ellipse is vertex , while in a circle is center.

Accepted Answer

False

Answer

True

Question 25

A parabola is defined by a fixed point called the focus and a fixed line called the directrix.

Accepted Answer

True

Answer

False

Question 26

The indicator to determine equation of an ellipse is a < b.

Accepted Answer

False

Answer

True

Question 27

In the standard equation of an ellipse when the denominator of the x-part is greater than the denominator of the y-part, the orientation of its graph is horizontal.

Accepted Answer

True

Answer

False

Question 28

The vertices are points on the ellipse collinear with the center and foci.

Accepted Answer

True

Answer

False

Question 29

If we have $$\left(x+2\right)^2=-\frac{3}{4}\left(y-2\right),$$ the parabola is opens upward.

Accepted Answer

False

Answer

True

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