What is the length of the chord intercepted b | vedclass

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(A) To find the length of the chord,we first find the points of intersection of the parabola $y = x^2 + 3x$ and the line $y = 5 - x$.Equating the two

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$6\sqrt{2}$

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(A) To find the length of the chord,we first find the points of intersection of the parabola $y = x^2 + 3x$ and the line $y = 5 - x$.Equating the two expressions for $y$:$x^2 + 3x = 5 - x$$x^2 + 4x - 5 = 0$$(x + 5)(x - 1) = 0$So,$x = 1$ and $x = -5$.For $x = 1$,$y = 5 - 1 = 4$. Point is $(1, 4)$.For $x = -5$,$y = 5 - (-5) = 10$. Point is $(-5, 10)$.The length of the chord is the distance between $(1, 4)$ and $(-5, 10)$:$L = \sqrt{(-5 - 1)^2 + (10 - 4)^2}$$L = \sqrt{(-6)^2 + (6)^2}$$L = \sqrt{36 + 36} = \sqrt{72} = 6\sqrt{2}$.

What is the length of the chord intercepted by the parabola $y = x^2 + 3x$ on the line $x + y = 5$?

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