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Write equation in standard form. Find center, radius, intercepts, and graph the circle.

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Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle. x^2+y^2+10x−18y=−102

asked Nov 20, 2013 in ALGEBRA 2 by linda Scholar

2 Answers

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Giiven equation x^2+y^2+10x-18y = -102

x^2+10x+y^2-18y = -102

Add 106 to each side.

x^2+10x+y^2-18y+106 = -102+106

x^2+10x+y^2-18y+25+81 = 4

x^2+10x+25+y^2-18y+81 = 4

(x+5)^2+(y-9)^2 = 4

(x-(-5))^2+(y-9)^2 = 4

Compare standard form of circle equation (x-h)^2+(y-k)^2 = r^2

radius is 2.

Center is (-5,9)

To find x intercept substitute y = 0 in given equation.

x^2+10x = -102

x^2+10x+102 = 0

x = [-10±√100-4*1*102]/2

x = [-10±√-408]/2

Squre root negitive is not possible.

There is no x intercept.

To find y intercept substitute y = 0 in given equation.

y^2-18y= -102

y^2-18y+102 = 0

y = [18±√324-4*1*102]/2*1

y = [18±√-84]/2

Squre root negitive is not possible.

There is no y intercept.

answered Jan 17, 2014 by ashokavf Scholar
0 votes

Standard form of a circle equation is image

Where center is (h ,k ) and radius of circle is r .

image

image

To change the expression into a perfect square  add (half the x coefficient)² and add (half the y coefficient)²to each side of the expression.

Here x coefficient = 10. so, (half the x coefficient)² = (10/2)2= 25

Here y coefficient = -18. so, (half the y coefficient)² = (-18/2)2= 81

Add 25 and 81 to each side

image

image ----> (1)

image

Compare it to standard form of circle image

image

To find intercept substitute x = 0 in the equation (1).

image

image

image

image

Negative squre root is imaginary,So there is no y  - intercept.

To find x  intercept substitute y  = 0 in the equation (1).

image

image

image

image

Negative squre root is imaginary,So there is no x - intercept.

Center at (-5,9) and r = 2,So we plot

Up (-5, 9+2) = (-5, 11)

Down (-5, 9-2) = (-5, 7)

Left (-5-2, 9) = (-7, 9)

Right (-5+2, 9) = (-3, 9)

Graph

1. draw the coordinate plane.

2. Plot the center at (-5,9).

3. Plot 4 points " radius away from the center in the up, down, left and right direction.

4. Sketch the circle.

answered May 23, 2014 by lilly Expert

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