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

Answer 1

#(x-4)^2#+ #(y-11/3)^2# =#34/9#

The general equation of a circle is #(x-a)^2# + #(y-b)^2#=#r^2# Where (a,b) is the centre of the circle and r is the radius.
So (a,b) is on the line y=#2/3# x +1 Substituting b=#2/3#a+1. Equation 1
(5,2) is on the circle so #(5-a)^2# +#(2-b)^2#=#r^2#. Equation 2
(3,2) is on the circle so #(3-a)^2#+#(2-b)^2# =#r^2# Equation 3
Subtract equation 3 from equation 2 gives #(5-a)^2# -#(3-a)^2# =0

Multiply out and simplify gives a= 4

Substitute in equation 1 gives b= #11/3#
Substitute in equation 2 gives #r^2# =#34/9#

Put all values into equation 3 as a check.

Yes it is correct

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Answer 2

The equation of the circle is (x - 3)(x - 5) + (y - 2)(y - 2) = 0.

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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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