Math

CalculusPrecalculus: Mathematics for Calculus - 6th EditionThe radius of the circles and distance between their centers. ( i ) ( x − 2 ) 2 + ( y − 1 ) 2 = 9 ( x − 6 ) 2 + ( y − 4 ) 2 = 16 ( i i ) x 2 + ( y − 2 ) 2 = 4 ( x − 5 ) 2 + ( y − 14 ) 2 = 9 ( i i i ) ( x − 3 ) 2 + ( y + 1 ) 2 = 1 ( x − 2 ) 2 + ( y − 2 ) 2 = 25 And interpret whether the circles intersect or not.Start your trial now! First week only $4.99!*arrow_forward*

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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.8, Problem 121E

To determine

**To calculate: **The radius of the circles and distance between their centers.

And interpret whether the circles intersect or not.

Expert Solution

The radius of the circles and distance between their centers is provided below,

**Given information:**

The pair of equation of circles,

**Formula used:**

The standard form of the equation of the circle is

Distance

**Calculation:**

Consider the equation,

Rewrite the equation

Recall that the standard form of the equation of the circle is

Compare,

Here,

Therefore, center of circle is

Next, rewrite the equation

Recall that the standard form of the equation of the circle is

Compare,

Here,

Therefore, center of circle is

Now, distance between the centers of the circle is computed below,

Recall that the distance

Evaluate the distance between

Now, sum of radius of two circles is

When the distance between the two centers of the circle is less than sum of radius of two circles then the two circles intersect each other.

Therefore, the circles

Consider the equation,

Rewrite the equation

Recall that the standard form of the equation of the circle is

Compare,

Here,

Therefore, center of circle is

Next, rewrite the equation

Compare,

Here,

Therefore, center of circle is

Now, distance between the centers of the circle is computed below,

Recall that the distance

Evaluate the distance between

Now, sum of radius of two circles is

When the distance between the two centers of the circle is less than sum of radius of two circles then the two circles intersect each other.

Therefore, the circles

Consider the equation,

Rewrite the equation

Compare,

Here,

Therefore, center of circle is

Next, rewrite the equation

Compare,

Here,

Therefore, center of circle is

Now, distance between the centers of the circle is computed below,

Recall that the distance

Evaluate the distance between

Now, sum of radius of two circles is

When the distance between the two centers of the circle is less than sum of radius of two circles then the two circles intersect each other.

Therefore, the circles

Therefore, the above results are summarized as,

To determine

**To explain: **Whether the circles intersect each other or not provided their radius and distance between their centers.

Expert Solution

**Given information:**

The pair of equation of circles.

Consider the equation,

Rewrite the equation

Compare,

Here,

Therefore, center of circle is

Next, rewrite the equation

Compare,

Here,

Therefore, center of circle is

Now, distance between the centers of the circle is computed below,

Evaluate the distance between

Now, sum of radius of two circles is

Therefore, the circles

Now, in general terms if d is the distance between the center of two circles with radius

When distance between the two centers of the circle is equal to sum of radius of two circles that is

When distance between the two centers of the circle is equal to sum of radius of two circles that is