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# help graphs

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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

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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

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