A parabola with a vertical axis has its vertex at the origin and passes through point (7,7). The parabola intersects line $$y = 6$$ at two points. The length of the segment joining these points is

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Uniteasy Admin · Accepted Answer

Since it has its vertex at the origin, the parabola has the following expression
$$y =kx^2 $$
Since it  passes through point (7,7),
$$k=7/7^2=1/7$$ 
$$y = x^2/7$$
The parabola intersects line $$y = 6$$ at two points. 
$$6 =x^2/7$$
$$x=\pm\sqrt{42}  $$
The length of the segment joining these points is
$$l = 4\sqrt{7} \approx 13 $$

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