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

Answer 1

The equation of the circle is #(x-32)^2+(y-60)^2=3650#

Let the center of the circle be #(a,b)# and radius r Then the equation of the circle is #(x-a)^2+(y-b)^2=r^2#
Then, #(3-a)^2+(7-b)^2=r^2# and #(7-a)^2+(5-b)^2=r^2#
Equqting the equations #(3-a)^2+(7-b)^2=(7-a)^2+(5-b)^2# developing, #9-6a+a^2+49-14b+b^2=49-14a+a^2+25-10b+b^2#
#9-6a-14b=25-14a-10b# #8a-4b=16# #2a-b=4# this is equation 1 Also, #y=(7x)/4+4# So #b=(7a)/4+4# Solving for a and be, we get #a=32# and #b=60# We calculate the radius #r^2=(7-32)^2+(5-60)^2#
#r^2=25^2+55^2##=># #r=60.41#
Equation of circle is #(x-32)^2+(y-60)^2=3650#
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Answer 2

The equation of the circle is ( (x - 5)^2 + (y - 3)^2 = 13 ).

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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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