BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 105RE
To determine

To calculate:The equation for the given circle with center (5,1) and which also passes through the origin.

Expert Solution

Answer to Problem 105RE

The equation for the given circle with center (5,1) and passing through origin is:

  x2+y2+10x+2y=0

Explanation of Solution

Given information:

A circle with center (h,k)=(5,1) and it passes through origin.

Formula used:

For a given circle with center (h,k) and radius r the equation is given as:

  (xh)2+(yk)2=r2

This is referred to as the Standard form for the equation of a given circle.

But, when an extra condition that is the circle passes through origin is imposed on the standard equation then with the help of distance formula to get D between two points say (x1,y1) and (x2,y2) is given as:

  D=(x2x1)2+(y2y1)2

Then we get r2=h2+k2

Putting this in standard equation we get:

The equation for the given circle with center (h,k) and which also passes through the origin is:

  (xh)2+(yk)2=h2+k2

Calculation:

Consider the given circle with center (h,k)=(5,1) and passing through origin.

Recall that the equation for the given circle with center (h,k) and which also passes through the origin is:

  (xh)2+(yk)2=h2+k2

Therefore, replacing the values we get:

  (x(5))2+(y(1))2=(5)2+(1)2(1)

Now using the following formulae:

  (a+b)2=a2+2ab+b2(ab)2=a22ab+b2

Then, (1) reduces to:

  x2+25+10x+y2+1+2y=25+1x2+y2+10x+2y+26=26x2+y2+10x+2y+2626=0x2+y2+10x+2y=0

Hence, the equation for the given circle with center (5,1) and passing through origin is:

  x2+y2+10x+2y=0

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!