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# Parabola

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The line x = k intersects the graph of the parabola x = -2y^2 - 3y + 5 - y^2 + 1 at exactly one point. What is k?

Jun 17, 2022

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What is k?

Hello Guest!

$$x = -2y^2 - 3y + 5 - y^2 + 1\\ \frac{dx}{dy}=-4y-3-2y=0\\ -6y=3\\ y_{extr}=-\frac{1}{2}$$

$$x_{max}=k=-\frac{1}{2}+\frac{3}{2}+5-\frac{1}{4}+1\\ \color{blue}k=6\frac{3}{4}$$

!

Jun 17, 2022
edited by asinus  Jun 17, 2022