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

Guest May 21, 2023

#1**0 **

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)).

Guest May 21, 2023

#2**0 **

*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 x^{2} + y^{2} = r^{2}

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.

x^{2} + y^{2} = r^{2}

7^{2} + y^{2} = [sqrt(130)]^{2}

49 + y^{2} = 130

y^{2} = 130 – 49

y^{2} = 81

y = __+__9

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

_{.}

Guest May 22, 2023