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# Parametric Parabola

+4
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Hi everyone,
I know that i am just being lazy or blind or both but the last question on this sheet eludes me.

140211 Tom's question.jpg
Feb 11, 2014

#1
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You need to show that T and U have the same y coordinate.

T has y coordinate apq
U has y coordinate -apr

but if you look at the coordinates of P and Q and note that PQ is perpendicular to the axis of the parabola then it should be clear that q = -r

so both T and U have y coordinates apq and thus TU is horizontal and thus perpendicular to the vertical parabola axis.
Feb 11, 2014
#2
+115747
+5
Rom:

You need to show that T and U have the same y coordinate.

T has y coordinate apq
U has y coordinate -apr

but if you look at the coordinates of P and Q and note that PQ is perpendicular to the axis of the parabola then it should be clear that q = -r

so both T and U have y coordinates apq and thus TU is horizontal and thus perpendicular to the vertical parabola axis.

Of course, thanks Rom, much appreciated.
Feb 11, 2014