Question

a. Find an equation for the line tangent to the circle $x^{2}+y^{2}=25$ at the point (3,-4) . (See the figure.) b. At what other point on the circle will a tangent line be parallel to the tangent line in part (a)?

Name: Problem 86, Chapter 1: College Algebra
Uploaded: 2020-07-27T05:10:58-08:00
Duration: 3 min 35 s
Channel: Ankit Gupta
Description: a. Find an equation for the line tangent to the circle x^2+y^2=25 at the point (3,-4) . (See the figure.) b. At what other point on the circle will a tangent line be parallel to the tangent line in part (a)?

   a. Find an equation for the line tangent to the circle $x^{2}+y^{2}=25$ at the point (3,-4) . (See the figure.)
b. At what other point on the circle will a tangent line be parallel to the tangent line in part (a)?

College Algebra

James Stewart,… 7th Edition

Chapter 1, Problem 86

Instant Answer

Solved by Expert Ankit Gupta

07/27/2020

Step 1

Step 1: The slope of the line from the origin (0,0) to the point (3,-4) is given by $m = \frac{0 - (-4)}{0 - 3} = -\frac{4}{3}$. Show more…

Show all steps

Thanks for your feedback!

a. Find an equation for the line tangent to the circle $x^{2}+y^{2}=25$ at the point (3,-4) . (See the figure.) b. At what other point on the circle will a tangent line be parallel to the tangent line in part (a)?

Play audio

Feedback

Ankit Gupta and 63 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Parallel Lines

In coordinate geometry, two lines are parallel if they have identical slopes. When a problem requires finding a tangent line on a circle that is parallel to a given tangent line, one utilizes the condition that their slopes must be equal, leading to equations that determine the points of tangency.

Implicit Differentiation

A method for finding derivatives of equations where y is not isolated as a function of x. For curves defined implicitly, such as circles, differentiating both sides of the equation with respect to x while treating y as a function of x allows us to determine the slope of the tangent line at any point on the curve.

Tangent Line to a Curve

A tangent line touches a curve at exactly one point and has the same slope as the curve at that point. For a circle, the tangent line at any point is perpendicular to the radius drawn to that point, providing a geometric relationship to verify or find the tangent's slope.

Please give Ace some feedback