To calculate:The equation for the circle and line in the given figure.
Answer to Problem 130RE
The equation for the circle and line in the figure are
Explanation of Solution
Given information:
The point
Formula used:
For a given circle with center
This is referred to as the Standard form for the equation of a given circle.
The general equation for the circle is:
Where
The distance
Slope m of the line passing through two points in general say
Slope-intercept equation for a given line which has slope as
Two-intercept equation for a given line which has
When two lines are perpendicular then the product of their slopes is zero that is
When two lines are parallel then their slope are equal that is
Calculation:
From the given figure it is clear that center of the circle is
Recall for a given circle with center
Therefore, replacing the values we get:
Now to find radius
Recall, the distance
Before applying distance formula the following must be known:
Therefore,
Hence radius
Put this value in
Recall the identities:
Use this to get:
Hence, the equation for the given circle is
Now for the equation of line:
Recall, slope m of the line passing through two points in general say
As it is known:
Therefore, slope of line is:
Slope of line is
And it passes through
Put these values in the general equation for the line which is
Which gives:
Now put
Thus, required equation of line is
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning