The points of intersection of the parabolas y | vedclass

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Question

(C) Given equations of parabolas:$y^2=5x$  $(i)$$x^2=5y$  (ii)From equation (ii),we get $y = \frac{x^2}{5}$.Substituting this into equation $(i)$:$(\f

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$x-y=0$

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(C) Given equations of parabolas:$y^2=5x$  $(i)$$x^2=5y$  (ii)From equation (ii),we get $y = \frac{x^2}{5}$.Substituting this into equation $(i)$:$(\frac{x^2}{5})^2 = 5x$$\frac{x^4}{25} = 5x$$x^4 = 125x$$x^4 - 125x = 0$$x(x^3 - 125) = 0$This gives $x = 0$ or $x^3 = 125$,which implies $x = 5$.If $x = 0$,then $y = 0$. If $x = 5$,then $y = \frac{5^2}{5} = 5$.The points of intersection are $(0,0)$ and $(5,5)$.Checking the options,both points satisfy the line $x - y = 0$.

The points of intersection of the parabolas $y^2=5x$ and $x^2=5y$ lie on the line

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