meganfrese
Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Consider the circle of radius 5 centered at (0,0). Find an equation of the line tangent to the circle at point (3,4). The book gives me the answer: y=-3/4(x-3) but can you explain to me how you get this answer?

Sagot :

pepe11
equation of the circle: x² + y² = 25
9 + 16 = 25 => the point (3,5) is on the circle.
the line tangent to the circle is perpendicular to the radius O point
slope of the radius: 4/3 => slope of the tangent = -3/4
tangent contain (3,4) and have -3/4 as slope.
so equation is : y - 4 = -3/4 (x - 3) => y = -3/4x - 4 + 9/4 + 4 => y = -3/4x + 9/4 
or y = -3/4(x-3) 
Blacklash

Answer:

The equation of the line tangent to the circle at point (3,4) is [tex](y-4)=-\frac{3}{4}(x-3)[/tex]

Step-by-step explanation:

First let us find equation of line passing through center of circle (0,0) and point(3,4)

We have

             [tex](y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\(y-0)=\frac{4-0}{3-0}(x-0)\\\\y=\frac{4}{3}x[/tex]

         Slope [tex]=\frac{4}{3}[/tex]

This line is perpendicular to line tangent to the circle at point (3,4).

Product of slopes of perpendicular lines = -1

Slope of tangent line [tex]=\frac{-1}{\frac{4}{3}}=-\frac{3}{4}[/tex]

So the equation of the line tangent to the circle at point (3,4) is given by

             [tex](y-y_1)=m(x-x_1)\\\\(y-4)=-\frac{3}{4}(x-3)[/tex]

The equation of the line tangent to the circle at point (3,4) is [tex](y-4)=-\frac{3}{4}(x-3)[/tex]

         

We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.