Start your trial now! First week only $4.99!*arrow_forward*

BuyFind*launch*

6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1, Problem 129RE

To determine

**To calculate:**The equation for the circle and line in the given figure.

Expert Solution

The equation for the circle and line in the figure are

**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 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

Therefore, the required equation for circle is:

**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 radius for above values is:

Now as the tangent is perpendicular to the circle, therefore the product of their slopes 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 **