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use the informaiton provided to write the genral conic form equation of each circle

1. three points on the circle: (7, -4), (-3,-4) and ( 6,-7)

indentify the center and radius of each. then sketch the graph

x^2+y^2-4x-14=0

 Mar 18, 2020

Best Answer 

 #1
avatar+20802 
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Let A = (7,-4), B = (-3,-4), and C = (6,-7).

Then, consider the two segments AB and BC.

The perpendicular bisectors of these two segments meet at the center of the circle.

1) Find the midpoint of AB and the slope of AB.

    Using the midpoint that you just found and the negative reciprocal of the slope that you just found,

    find the equation of the line which is the perpendicular bisector of AB.

2) Repeat the steps of part 1 to find the perpendicular bisector of BC.

3) Use those two equations to find the point where they intersect. 

    This will be the center of the circle.

4) To find the radius of the circle, use the distance formula for the center of the circle and one of the 

    three given points.

5) You now have the center and the radius; use these values to find the equation of the circle.

 Mar 18, 2020
 #1
avatar+20802 
+1
Best Answer

Let A = (7,-4), B = (-3,-4), and C = (6,-7).

Then, consider the two segments AB and BC.

The perpendicular bisectors of these two segments meet at the center of the circle.

1) Find the midpoint of AB and the slope of AB.

    Using the midpoint that you just found and the negative reciprocal of the slope that you just found,

    find the equation of the line which is the perpendicular bisector of AB.

2) Repeat the steps of part 1 to find the perpendicular bisector of BC.

3) Use those two equations to find the point where they intersect. 

    This will be the center of the circle.

4) To find the radius of the circle, use the distance formula for the center of the circle and one of the 

    three given points.

5) You now have the center and the radius; use these values to find the equation of the circle.

geno3141 Mar 18, 2020

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