SOLUTION: Does (1,11) lie on the parabola defined by the focus (0,4) and the directrix y = x?

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Question 1157987: Does (1,11) lie on the parabola defined by the focus (0,4) and the directrix y = x?
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The point lies on the parabola if the distance from the point to the focus is equal to the distance from the point to the directrix.

The distance from (1,11) to (0,4) is sqrt%281%5E2%2B7%5E2%29+=+sqrt%2850%29+=+5sqrt%282%29

To find the distance from (1,11) to the directrix y=x, use the point-to-line distance formula.

abs%28%281-11%29%2Fsqrt%281%5E2%2B1%5E2%29%29+=+10%2Fsqrt%282%29+=+5sqrt%282%29

ANSWER: Yes, the point (1,11) is on that parabola.