Is the point (11,5) on the parabola? Show or explain your work.

The point (11, 5) is NOT on the parabola.

Step-by-step explanation:

Let be any point on the parabola

Let be the focus

Let be the the directrix

Distance between and the focus:

Distance between and the directrix is

Given:

Therefore:

Distance between and the focus:

Distance between and the directrix is

Equate the two expressions and solve for :

Now rewrite with (x, y):

Therefore, this is the equation of the parabola

To determine if the point (11, 5) is on the parabola, input x = 11 into the equation:

So the point (11, 5) is NOT on the parabola.

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step-by-step explanation:

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