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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the definition of a normal line?
💡 Hint: Think about the relationship between tangents and normals.
Question 2
Easy
If the slope of the tangent is 3, what is the slope of the normal?
💡 Hint: Remember the relationship between slopes of perpendicular lines.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the slope of a normal line if the slope of the tangent is 5?
- -1/5
- -5
- 1/5
💡 Hint: Recall the formula for slopes of perpendicular lines.
Question 2
True or False: The normal line intersects the curve at more than one point.
- True
- False
💡 Hint: Think about the definition of a normal line.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the normal line to the circle x^2 + y^2 = r^2 at the point (rcos(θ), rsin(θ)) is perpendicular to the tangent line.
💡 Hint: Construct the derivative of the curve to find the slopes.
Question 2
Derive the equation of a normal line to a parabola y = x^2 at the vertex.
💡 Hint: Consider what happens to slopes at extremities.
Challenge and get performance evaluation