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A circle is centered at the origin and has a radius of square root 130. Work out the coordinates of the two points on the circle where x=7

 May 21, 2023
 #1
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To find the coordinates of the two points on the circle where x = 7, we need to substitute x = 7 into the equation of the circle and solve for the corresponding y-coordinates.

The equation of a circle centered at the origin with radius sqrt{130} is given by x^2 + y^2 = 130^2 = 16900.

 

Substituting x = 7 into the equation, we have:

49 + y^2 = 16900.

Then y^2 = 16900 - 49 = 16851, so y = +/- sqrt(16851).

 

The coordinates of the two points on the circle are then (7,sqrt(16851)) and (7,-sqrt(16851)).

 May 21, 2023
 #2
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A circle is centered at the origin and has a radius of square root 130. Work out the coordinates of the two points on the circle where x=7  

 

The first answer made a mistake.  

Used 130 for r instead of sqrt(130).  

The numbers got really big after that.  

 

The equation of a circle centered at the origin is x2 + y2 = r2   

 

We already know the x coordinate is 7, because the problem tells us that, 

so we only have to solve for y.  So plug the 7 in for x and sqrt(130) in for r  

into the equation.  

 

                                                                       x2 + y2  =  r2   

 

                                                                       72 + y2  =  [sqrt(130)]2  

 

                                                                       49 + y2  =  130  

 

                                                                               y2  =  130 – 49  

 

                                                                               y2  =  81  

 

                                                                               y   =  +9  

 

So the coordinates are                                  (7, 9) and (7, –9)  

.

 May 22, 2023

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