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worty [1.4K]
2 years ago
10

Write the equation of the circle below to complete the square. Also determine the area of the circle.

Mathematics
1 answer:
diamong [38]2 years ago
8 0

Answer: (x-7)^2+(y+2)^2=11^2 ; A=121\pi

Step-by-step explanation:

I have never done a problem like this, so this is my first time attempting it.

The standard form for the equation of a circle is:

(x-a)^2+(y-b)^2=r^2

Begin by grouping the 'x' terms and 'y' terms:

(x^2-14x)+(y^2+4y-68)=0

Complete the square for the second polynomial:

(\frac{b}{2} )^2=(\frac{4}{2} )^2=4

(x^2-14x)+(y^2+4y+4-4-68)=0

(x^2-14x)+(y^2+4y+4)-4-68=0

(x^2-14x)+(y^2+4y+4)-72=0

(x^2-14x)+(y+2)^2-72=0

Do the exact same process with the other polynomial:

(x^2-14x-72)+(y+2)^2=0

Complete the square:

(\frac{14}{2} )^2=49

(x^2-14x+49-49-72)+(y+2)^2=0

(x^2-14x+49)-49-72+(y+2)^2=0

(x^2-14x+49)-121+(y+2)^2=0

(x-7)^2-121+(y+2)^2=0

Bring the 121 to the other side to get:

(x-7)^2+(y+2)^2=121

(x-7)^2+(y+2)^2=11^2

The above expression is the equation of our circle in standard form. It is centered at the coordinates (7, -2) and has a radius of 11 units. The area of a circle if given by:

A=\pi r^2=121\pi

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