Two parabolas have the same focus. If their d | vedclass

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(A) Let the common focus be $(h, k)$.The equation of a parabola with focus $(h, k)$ and directrix $L = 0$ is $(x - h)^2 + (y - k)^2 = L^2$.For the fir

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$\pm 1$

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(A) Let the common focus be $(h, k)$.The equation of a parabola with focus $(h, k)$ and directrix $L = 0$ is $(x - h)^2 + (y - k)^2 = L^2$.For the first parabola with directrix $y = 0$ (the $x$-axis),the equation is $(x - h)^2 + (y - k)^2 = y^2$.For the second parabola with directrix $x = 0$ (the $y$-axis),the equation is $(x - h)^2 + (y - k)^2 = x^2$.To find the common chord,we subtract the two equations:$((x - h)^2 + (y - k)^2 - y^2) - ((x - h)^2 + (y - k)^2 - x^2) = 0$This simplifies to $x^2 - y^2 = 0$,which implies $x^2 = y^2$,or $y = \pm x$.Thus,the slopes of the common chords are $m = 1$ and $m = -1$,which can be written as $\pm 1$.

Two parabolas have the same focus. If their directrices are the $x$-axis and the $y$-axis respectively,then the slope of their common chord is:

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