If the lines y = x and y = -x intersect the p | vedclass

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(B) Given the parabola $y^2 = 4x$. For the line $y = x$,substituting $y$ in the parabola equation: $x^2 = 4x \implies x(x - 4) = 0$. Since $x 
eq 0$,

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) Given the parabola $y^2 = 4x$. For the line $y = x$,substituting $y$ in the parabola equation: $x^2 = 4x \implies x(x - 4) = 0$. Since $x 
eq 0$,we have $x = 4$,so $y = 4$. Thus,point $A = (4, 4)$. For the line $y = -x$,substituting $y$ in the parabola equation: $(-x)^2 = 4x \implies x^2 = 4x \implies x(x - 4) = 0$. Since $x 
eq 0$,we have $x = 4$,so $y = -4$. Thus,point $B = (4, -4)$. The length of $AB$ is the distance between $(4, 4)$ and $(4, -4)$. $AB = \sqrt{(4 - 4)^2 + (4 - (-4))^2} = \sqrt{0^2 + 8^2} = 8$.

If the lines $y = x$ and $y = -x$ intersect the parabola $y^2 = 4x$ at points $A$ and $B$ respectively,other than the origin,what is the length of $AB$?

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