A circle has a center that falls on the line #y = 4/7x +6 # and passes through # ( 2 ,1 )# and #(3 ,5 )#. What is the equation of the circle?

Answer 1

The equation of the circle is #(x+70/23)^2+(y-98/23)^2=19081/529#

Let #C# be the mid point of #A=(2,1)# and #B=(3,5)#
#C=((2+3)/2,(1+5)/2)=(5/2,3)#
The slope of #AB# is #=(5-1)/(3-2)=(4)/(1)=4#
The slope of the line perpendicular to #AB# is #=-1/4#
The equation of the line passing trrough #C# and perpendicular to #AB# is
#y-3=-1/4(x-2)#
#y=-1/4x+1/2+3=-1/4x+7/2#
The intersection of this line with the line #y=4/7x+6# gives the center of the circle.
#-1/4x+7/2=4/7x+6#
#1/4x+4/7x=7/2-6#
#23/28x=-5/2#
#x=-28/23*5/2=-70/23#
#y=4/7*(-70/23)+6=98/23#
The center of the circle is #(-70/23,98/23)#

The circle's radius is

#r^2=(2+70/23)^2+(1-98/23)^2#
#=(116/23)^2+(75/23)^2#
#=19081/529#

The circle's equation is

#(x+70/23)^2+(y-98/23)^2=19081/529#

graph{ [-36.54, 36.55, -18.26, 18.28]} = ((x+70/23)^2+(y-98/23)^2-19081/529)(y-4/7x-6)(y+1/4x-7/2)=0

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Answer 2

The equation of the circle is ( (x - 3)^2 + (y - 5)^2 = \frac{5}{2} ).

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Answer from HIX Tutor

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.

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.

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