Tangent Line Problem Concepts

Tangent Line Problem Concepts

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
8.EE.C.7B, HSA.REI.A.2, HSA.APR.A.1

+1

Standards-aligned

Created by

Amelia Wright

FREE Resource

Standards-aligned

CCSS.8.EE.C.7B
,
CCSS.HSA.REI.A.2
,
CCSS.HSA.APR.A.1
CCSS.7.EE.B.3
,
The video tutorial explains how to find the slope of a line tangent to both a circle and a hyperbola. It begins with a clarification on the y-intercept and the importance of taking the principal root. The tutorial then sets constraints from both the circle and hyperbola, equates them, and solves for the slope m. The process involves squaring both sides of the equation, simplifying, and using the quadratic formula to find the solution. The video emphasizes understanding the underlying math concepts rather than memorizing formulas.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is it important for the y-intercept to be positive in the tangent line problem?

To align with the x-axis

To avoid complex numbers

To make the equation easier to solve

To ensure the line has a positive slope

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving for the slope m in the tangent line problem?

Finding the midpoint

Equating constraints from the circle and hyperbola

Taking the derivative

Using the quadratic formula

Tags

CCSS.8.EE.C.7B

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What operation is performed after equating the constraints from the circle and hyperbola?

Differentiating the equation

Integrating the equation

Squaring both sides of the equation

Taking the logarithm

Tags

CCSS.HSA.REI.A.2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of isolating the radical on one side of the equation?

To convert it into a linear equation

To find the x-intercept

To eliminate the variable m

To simplify the equation

Tags

CCSS.8.EE.C.7B

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of equation is formed after simplification in the tangent line problem?

Linear equation

Exponential equation

Quadratic equation

Logarithmic equation

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the quadratic equation in the tangent line problem solved?

By factoring

Using the quadratic formula

By completing the square

Using substitution

Tags

CCSS.8.EE.C.7B

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the significance of the number 495 in the quadratic equation?

It is the constant term

It is the coefficient of m squared

It is the coefficient of m to the fourth

It is the solution to the equation

Tags

CCSS.HSA.APR.A.1

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