Parabola, tangent/normal with axis

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
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
12 Replies
iTeachChem Helper
@Apu
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coolguy.
coolguy.3mo ago
@Nimboi [ping if answering] I think after finding t you can find any one dist to get focal dist
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coolguy.
coolguy.3mo ago
You'll need to know this property though
Nimboi [ping if answering]
ah hang on, what property did you use here?
coolguy.
coolguy.3mo ago
Basically those base angles of triangle 1 are equal and base angles of triangle 2 are equal - cengage gives it clearly
Nimboi [ping if answering]
alr ill look it up in a bit 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
coolguy.
coolguy.3mo ago
It ain't foot of perpendicular see carefully
Nimboi [ping if answering]
oh mb assumption baseless
coolguy.
coolguy.3mo ago
Isokay
Nimboi [ping if answering]
ah +solved coolguy.
iTeachChem Helper
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