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Chapter 8: Q. 2 (page 556)

Find an equation for the circle with center at the point (-5,1)and radius 3. Graph this circle.

Short Answer

Expert verified
  • The equation of the circle is (x+5)2+(y-1)2=9.
  • The graph is

Step by step solution

01

Step 1. Given Information

  • The center of the circle is (-5,1).
  • The radius is 3.
02

Step 2. Find the Equation

  • The general equation of a circle is (x-h)2+(x-k)2=r2.
  • Substitute h=-5,k=1into the general equation and simplify.

localid="1647407263863" (x-(-5))2+(y-1)2=32(x+5)2+(y-1)2=9

03

Step 3. Find the Intercepts

  • Substitute 0 for xand find the y-intercepts.

(0+5)2+(y-1)2=9(y-1)2=-16

  • As the square is a negative value, there are no x-intercepts.
  • Substitute 0 for yand find the x-intercepts.

(x+5)2+(0-1)2=9 (x+5)2=8 x+5=±22x=-22-5,-22+5

04

Step 4. Plot the Graph

Use the center and the intercepts to plot the circle.

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