A circle has a center that falls on the line #y = 6/7x +7 # and passes through # ( 7 ,8 )# and #(3 ,1 )#. What is the equation of the circle?
Equation of the circle:
Three equations (h, k, r) with three unknowns
Equations two and three allow us to eliminate r.
solve k:
calculate r:
The circle's equation
graph{(y101/14)^236205/784)(y6/7x7)=0[30,30,15,15]}
May God bless you all. I hope this explanation helps.
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The equation of a circle can be written in the form ((x  h)^2 + (y  k)^2 = r^2), where ((h, k)) is the center of the circle and (r) is the radius. To find the equation of the circle, we first need to find the center and then calculate the radius using the given points.

The center of the circle lies on the line (y = \frac{6}{7}x + 7). This means the coordinates of the center are of the form ((x, \frac{6}{7}x + 7)).

Since the center lies on the line, it must satisfy the equation of the line. Substitute the coordinates of the center into the equation of the line and solve for (x) to find the (x)coordinate of the center.

Once you have the (x)coordinate of the center, substitute it back into (y = \frac{6}{7}x + 7) to find the (y)coordinate of the center.

The radius of the circle can be found using the distance formula between the center and one of the given points. The distance formula is (d = \sqrt{(x_2  x_1)^2 + (y_2  y_1)^2}), where ((x_1, y_1)) are the coordinates of the center and ((x_2, y_2)) are the coordinates of one of the given points.

Once you have the center and the radius, you can write the equation of the circle using the form ((x  h)^2 + (y  k)^2 = r^2), where ((h, k)) is the center and (r) is the radius.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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