\begin{align*} (x+3)^2+(y-1)^2&=25\\ (x-3)^2+(y-1)^2&=16 \end{align*}

In the xy-plane, the two circles with the equations above intersect at points A and B. What is the equation of the line that contains both point A and point B ?

A)
B)
C)
D)

 

 

Comments (1)

Solving it in a different way:
Beginning from Step –
(x+3)^2 – 25 = (x-3)^2 – 16
(x+3)^2 – (x-3)^2 = 25 – 16 = 9

Using, a^2 – b^2 = (a – b)*(a+b), in the Left Hand Side of the equation, where a = (x+3) and b = (x-3), we get,

(x+3)^2 – (x-3)^2 = [(x+3) – (x-3)]*[(x+3) + (x-3)] = [(x+3-x+3)*(x+3+x-3)] = [(6)*(2x)] = 12x
Therefore, 12x = 9
x = 0.75

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