The line \(y = \frac{3x + 15}{4}\) intersects the circle \(x^2 + y^2 = 36\) at \(A\) and \(B\). Find the length of chord \(\overline{AB}\).

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Thank you very much!

Guest May 10, 2020

#1**0 **

Find the points of intersection of the line y = (3x + 15)/4 and the circle x^{2} + y^{2} = 36

and then determine the distance between them.

First, using substitution to find the points: x^{2} + [ (3x + 15)/4 ]^{2} = 36

x^{2} + (9x^{2} + 90x + 225)/16 = 36

16x^{2} + 9x^{2} + 90x + 225 = 576

25x^{2} + 90x - 351 = 0

Using the quadratic formula to find the values for x:

x_{1} = ( -90 + sqrt( 43200 ) ) / 50

x_{2} = ( -90 - sqrt( 43200 ) ) / 50

Substitue each value of x into the equation y = (3x + 15)/4 to get its corresponding y-value.

Then, use the distance formula to find the distance between these two points.

geno3141 May 10, 2020