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.
+505 (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
