Nonlinear Equations and Functions Questions for Tests and Worksheets

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Grade 11 Nonlinear Equations and Functions

What are the coordinates of the center of an ellipse defined by the equation

$16x^2+25y^2+160x-200y+400=0$ ?

(-5, 4)
(5, -4)
(5, 4)
(-5, -4)

Grade 11 Nonlinear Equations and Functions

Identify the following conic:

$x^2-4x-4y^2+8y=4$ .

Parabola
Circle
Hyperbola
Ellipse

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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Let

$(x,y)$ be a point on the hyperbola. What is the distance,

$d_1$ , between

$F_1$ and the point

$(x,y) ?$

$d_1 = sqrt( (x+c)^2 + y^2)$
$d_1 = sqrt( (x-c)^2 + y^2)$
$d_1 = sqrt( (x^2 + y^2)$
$d_1 = sqrt( (x-c)^2 + (y-c)^2)$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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Let

$(a,0)$ be the right vertex of the hyperbola. What is the distance between this vertex and

$F_1 ?$

$a-c$
$a+c$
$a$
$c$

Grade 11 Nonlinear Equations and Functions

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Squaring both sides, expanding, and combing like terms, dividing by any common constants, and putting all terms without a square root on the left side of the equation results in which of the following equations?

$2cx - a = 0$
$cx pm a^2 = -2 sqrt((x-c)^2 + y^2)$
$cx - a^2 = 0$
$cx - a^2 = pm a sqrt( (x-c)^2 + y^2)$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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Substitute the equations for

$d_1, d_2$ found in the second and third questions into the equation in the previous question. After some rearranging, the result is the following equation:

$sqrt( (x+c)^2 + y^2) = pm 2a + sqrt( (x-c)^2 + y^2)$

Why is there a plus-minus sign on the

$2a$ term?

In order to remove the absolute value sign, one has to consider the case where $d_1>d_2$ and $d_1 < d_2$ .
To remove the square root from this term, one has to look at the positive and negative case.
Since it's not certain which side of the equation this term should be on, it could be either positive or negative.
This is a hyperbola and the curves can be on either the positive or negative x-axis.

Grade 11 Nonlinear Equations and Functions

TRUE or FALSE. A conic section is represented by a

$li n ear$ equation.

True
False

Grade 11 Nonlinear Equations and Functions

A(n) is defined by a set of points in a plane that are equidistant from a fixed line and a fixed point not on the fixed line.

circle
parabola
ellipse
None of the Above

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.1

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Which of the following represents the length of the horizontal leg of the right triangle? (If need be, use the first correct answer in the first question if there were multiple correct answers.)

$3-x$
$x+3$
$|x-3|$
$(3-x)^2$

Grade 11 Nonlinear Equations and Functions

Identify the following shape.

$2x^2+3xy-y^2-10x-9y+5=0$

Circle
Hyperbola
Ellipse
Parabola

Grade 11 Nonlinear Equations and Functions

Solve

$x^3 = 216$ .

$x=9$
$x=6$
$x=81$
$x=27$

Grade 11 Nonlinear Equations and Functions CCSS: HSA-REI.A.2

Solve. Check for extraneous solutions.

$x/(x-1)=(x+3)/(-2x+2)$

$x=-1 or x=-2$
$x=-1$
$x=1$
$x=1 or x=-1$

Grade 10 Nonlinear Equations and Functions CCSS: HSA-REI.A.2

$(x-1)/x = 4$ , then

$x =$

$3$
$-3$
$-1/6$
$-1/3$

Grade 11 Nonlinear Equations and Functions

The equation

$x^2+y^2+2x+1=0$ represents

a point.
a circle.
a parabola.
an ellipse.

Grade 10 Nonlinear Equations and Functions

Find

$(2n^3)^2$ if

$(n+2)(n+3)=(4-n)(12-n)$ .

Grade 11 Nonlinear Equations and Functions

Identify the following shape.

$x^2+xy-y^2-10x-3y+5=0$

Circle
Hyperbola
Parabola
Ellipse

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.2

What is the equation of a parabola with the focus at

$(1,3)$ and a directrix of

$x=-5?$

$(x-3)^2 = 12(y+2)$
$(y-3)^2 = 12(x-1)$
$(y+3)^2 = 3(x-2)$
$(y-3)^2 = 12(x+2)$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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What does

$|d_1 - d_2|$ equal?

$|d_1 - d_2| = a$
$|d_1 - d_2| = c$
$|d_1 - d_2| = |a-c|$
$|d_1 - d_2| = 2a$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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What is the distance between

$F_2$ and the vertex

$(a,0) ?$

$c$
$a$
$c-a$
$a+c$

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

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What is the distance,

$d_2$ , between the

$F_2$ and the point

$(x,y) ?$

$d_2 = sqrt( (x-c)^2 + (y-c)^2)$
$d_2 = sqrt( x^2 + y^2)$
$d_2 = sqrt( (x+c)^2 + y^2)$
$d_2 = sqrt( (x-c)^2 + y^2)$

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