Parabola, tangent/normal with axis

[foggy thicket]

If (-2, 5) and (3, 7) are the points of intersection of the tangent and normal at a point on a parabola with the axis of the parabola, then the focal distance of that point is?

A. √29 / 2
B. 5 / 2
C. √29
D. 2 / 5

Ans is ||A||

[zealous raven]

<@&1227988399579730072>

Note for OP

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[dry quail]

@foggy thicket I think after finding t you can find any one dist to get focal dist

You'll need to know this property though

[foggy thicket]

ah hang on, what property did you use here?

[dry quail]

Basically those base angles of triangle 1 are equal and base angles of triangle 2 are equal - cengage gives it clearly

[foggy thicket]

alr ill look it up in a bit

[foggy thicket]

so any point's foot of perpendicular on the axis is the midpoint of the foot of the tangent and normal?

that's a really interesting symmetry

[dry quail]

It ain't foot of perpendicular see carefully

[foggy thicket]

oh mb

assumption baseless

[dry quail]

Isokay

[foggy thicket]

ah

+solved coolguy.