PRE-CALCULUS 2ND QUARTER EXAM

What is the center of the circle given by the equation (𝑦 − 7)^2 + (𝑥 + 2)^2 = 36 ?

(-2, 7)

Find the distance between points (8,1) and (-7,1).

15

These are intersections of both right circular cones and a plane that do not pass through the vertices of the cones.

Conic Section

What do you call if the x-axis and y-axis meet each other?

Ordered pair

How can you identify the center of the circle when it is not in the origin?

at (h,k)

Describe the opening of the parabola in the given equation y² = -x

Opens left

Describe the opening of the parabola in the given equation x² = -y

Opens down

What are the 4 conic sections?

• Cirlce

• Parabola

• Ellipse

• Hyperbola

How can you determine the direction a parabola opens based on the coefficient of the squared term in its standard form equation? 

The direction cannot be determined from the coefficient.

What is the length of the diameter of a circle?

Twice the length of the radius

How many foci does an ellipse have?

two

In an ellipse, if a = 13 and b = 5, what is the distance between the center and a focus?

12

What is the center of the hyperbola given by the equation? 

(x-2)² / 5 - (y-3)² / 7 = 1

(2, -3)

It denotes as the distance from center to vertex.

a

The line segment through the center, perpendicular to the principal axis and with endpoints on the ellipse.

Minor axis

What do you call the red dot?

Center

What do you call the yellow dots?

vertices

What do you call the broken red line connected from (-4, 0) to (4, 0)?

Major axis

What do you call the red line?

Principal Axis

What is the principal axis in hyperbola?

Transverse axis

What is transverse axis in Parabola?

Axis of symmetry

What do you call the yellow broken lines in parabola?

Axis of symmetry

What do you call the red dot?

Vertex

What do you call the brown line?

Latus rectum

What do you call the blue line?

Directrix

What do you call the blue dot?

Focus

What is the formula for foci of an ellipse?

c = √a²-b²

What is the formula for foci of a hyperbola?

c =√a²+b²

Based on the given figure, find the coordinates of the following: Center, Vertices, Co-vertices, Foci, Latera recta, Transverse axis, Conjugate axis.

Center: (-2,0)

Vertices: (-2, 2) (-2,-2)

Co-vertices: (-4, 0) (0,0)

Foci: (-2, 4) (-2, -4)

Latera recta: (-5,4) (1, 4) (-5, -4) (1, -4)

Transverse Axis: vertical x=-2

Conjugate Axis: horizontal from (-4, 0) to (0, 0)

What is the center of the circle given by the equation?

(x-7)² + (y+2)² = 36

(7, -2)

Describe the opening of the parabola in the given equation x² = y

Opens up

The distance from the vertex to the focus of a parabola is known as

The focal length

True or False:

Circle is a conic section

True

True or False (what’s the correct answer?):

The equation of a circle is always in the form x² + y² = r²

(x-h)² + (y-k)² = r²

True or False:

A circle has an eccentricity of 0.

True

True or False:

The center of a circle is the point where the x-coordinate and y-coordinate are both zero.

Any point (h, k)

True or False:

The radius of a circle can be positive and negative.

True

True or False:

The equation x² + y² = 16 represents a circle with radius 16.

r = 4

True or False:

The diameter of a circle is thrice the length of the radius.

Twice

True or False:

The radius square of a circle can be positive and negative.

Always positive

True or False:

x + 3² = -4y is an equation of parabola opens down.

(x+3)² = -4y

True or False:

(x-h)² + (y-k)² = r² is the standard form of a circle.

True

What is the standard form of a circle?

(x-h)² + (y-k)² = r²

It is defined as a two-dimensional coordinate plane, which is formed by the intersection of the x-axis and y-axis.

Cartesian plane

He is a French mathematician, philosopher, and theologian who invented the cartesian plane.

Rene Descartes

The x-axis and y-axis intersect perpendicular to each other at the point called?

Origin

When was Rene Descartes and when did he die?

1596-1650

Which quadrant is -4, 7?

Quadrant II

Which quadrant is 2, -8?

Quadrant IV

General form of a conic section

Ax² + Bxy + Cy² + Dx + Ey + F = 0

Which conic section is this?

4x² + 2y² - 13x + 3y - 15 = 0

Ellipse

Which conic section is this?

x² + y² + 8y - 33 = 0

Circle

Which conic section is this?

x + 4y² - 7x + 19y + 21 = 0

Parabola

Which conic section is this?

-9x² + 4y² + 2x - 11y - 141 = 0

Hyperbola

Which conic section is this?

2x² - 12x + 2y² - 6y - 24 = 0

Circle

Which conic section is this?

x + 4y² - 7x + 19y + 21 = 0

Parabola

 What do you call a line segment is from the center to its perimeter?

Radius

What do you call when a conic section is cut parallel to its side?

Parabola

What do you call that a line segment passes through center of the circle and whose endpoints lie on its arc?

Diameter

Which conic section best describes the graph of the given equation?

x² + y² + 2x - 4y + 5 = 0.

Point

What is the axis of symmetry of a parabola?

Line that divides the parabola into two symmetricl halves

Find the distance between points (-3,2) and (5,3).

√65

Find the equation of the parabola in the standard form if the equation of the parabola in the general form is given by y² - 2y - 12x - 23 = 0.

(y-1)² = 12(x+2)

Express the given equation in general form: (x-4)²+(y-4)²=24.

x² + y² - 8x - 8y + 8 = 0

What is the standard form of the equation for a parabola that opens right?

(y-k)² = 4p(x-h)

What does the sign in 4p of the parabolic equation determine?

Direction of opening

The fixed point that determines the shape of the parabola

Focus

The line perpendicular to the axis of symmetry

Directrix

What is the opening of the parabola?

(x-5)² = -24(y-1)

Opens down

What is the opening of the parabola?

(x+1)²=3(x-31)

Not a parabola

What is the opening of the parabola?

(y-100)² = (x+1)

Opens right

What is the opening of the parabola?

(y-5) = -24(x-1)²

Opens down

What is the opening of the parabola?

(x+21)² = 2(y-1)

Opens up