# A circle has a center that falls on the line #y = 7/6x +1 # and passes through #(9 ,4 )# and #(8 ,5 )#. What is the equation of the circle?

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The equation of the circle is ( (x - h)^2 + (y - k)^2 = r^2 ), where ( (h, k) ) is the center of the circle and ( r ) is the radius.

First, find the center of the circle using the given line equation: [ y = \frac{7}{6}x + 1 ] [ \frac{7}{6}x = y - 1 ] [ x = \frac{6}{7}(y - 1) ] [ h = \frac{6}{7}(k - 1) ]

Then, find the radius (( r )) using the distance formula between the center and one of the given points: [ r = \sqrt{(x_1 - h)^2 + (y_1 - k)^2} ]

Substitute the coordinates of one of the given points into the distance formula to find ( r ).

Finally, substitute the values of ( h ), ( k ), and ( r ) into the equation ( (x - h)^2 + (y - k)^2 = r^2 ) to get the equation of the circle.

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When evaluating a one-sided 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 one-sided 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 one-sided 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.

- A triangle has corners at #(2 ,4 )#, #(6 ,5 )#, and #(4 ,3 )#. What is the area of the triangle's circumscribed circle?
- A circle has a center that falls on the line #y = 5/3x +1 # and passes through #(8 ,2 )# and #(3 ,2 )#. What is the equation of the circle?
- What is the equation of the circle with a center at #(4 ,1 )# and a radius of #5 #?
- A triangle has corners at #(5 ,1 )#, #(3 ,9 )#, and #(4 ,7 )#. What is the area of the triangle's circumscribed circle?
- A circle has a center that falls on the line #y = 7/9x +7 # and passes through # ( 4 ,1 )# and #(3 ,7 )#. What is the equation of the circle?

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