The line 3x + 4y = 6 intersects the circle x^2 + y^5 = 25 at two points A and B.  Find the distance between A and B.

 Dec 25, 2020

(by the way, I'm assuming that you mean x^2+y^2=25, because or else it wouldn't be a circle)

First, set up a system of equations:

\(x^2+y^2=25 \\ 3x+4y=6 \)

notice that the second equation, 3x+4y=6, is very close to 3x+4y=25. 

The system of equations below:

\(x^2+y^2=25 \\ 3x+4y=25 \)

would have 2 solutions: (3,4) and (-3,-4). The distance between them is 10, as it is the diameter of the circle.

therefore, as the constant 25 in the equation 3x+4y = 25 decreases by 1, the distance between the equation with the number decreasing and the original equation 3x+4y=25 will increase by 10/50 = 1/5.

the rest of the explanation is in the photo below:

Answer: \(2\sqrt{23.56}\)

Approximate form: 9.708


I hope this helped you cuz i took a long time solving this lol

 Dec 27, 2020

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