Question

If any tangent to the ellipse \frac{X^2}{a^2} + \frac{Y^2}{b^2}=1 \) intercepts equal length \(L\) on the axes then find \( L\)

Sadly it took me more than 5 mints to solve this, how much do you take? ... Am I having intellectual atrophy?

Answer 1

If any tangent to the ellipse \( \frac{X^2}{a^2} + \frac{Y^2}{b^2}=1 \) intercepts equal length on the axes then find L

Sadly it took me more than 5 mints to solve this, how much do you take? ... Am I having intellectual atrophy?

Answer 2

Thanks for the medal zed, do you think it's a good problem? or am I just becoming slow? :(

Answer 3

I thought it was a good problem, but it is 1am here. xP

Answer 4

haha, well I am out practice so it seemed soo hard :D

Answer 5

saso, give it a shot!

Answer 6

seriously?

Answer 7

that's beyond me lol

Answer 8

lol, comeon it's not that hard, just High school stuffs :)

Answer 9

well at the moment, I know zero about ellipses or formulas related to them so that's like entering a new town and someone asks you for direction..

Answer 10

at the moment i have exams through out the next 2 weeks so no studying, just revision, after the exam when i start studying, i may come across ellipses and i may be able to solve it :) but if anyone does solve it, i'll take a look at the solution, will get a fair idea what the whole thing is about and when i get to study it, shouldn't be difficult :)

Answer 11

That's the spirit saso!

Answer 12

If I understand this correctly, the slope of the tangent must be 1 or -1 - is that right?

Answer 13

is this an example of what the question is asking?

Answer 14

assuming my interpretation of the question is correct, I think the answer is:\[L=\frac{a^2\pm b^2}{\sqrt{a^2+b^2}}\]

Answer 15

there are 4 possible tangents here

Answer 16

yes - I drew one example

Answer 17

if i understand x and y to be the points where the tangents cut the axes, then what's a and b?