Question

prove that the line x cosA+y sinA=p touches the hyperbola x^2\a^2-y^2\b^2=1 if p^2=a^2cos^2A-b^2 sin^2A .

Answer 1

So we have to use the condition of tangency of a line to a given curve

Answer 2

ok I solved the problem. @Loser66 did you solve it?

Answer 3

show me , please. I don't know how to

Answer 4

ok here is my solution @Loser66 @Ambuj

Answer 5

I don't get how you get from \(Y-y=\dfrac{x}{y}\dfrac{b^2}{a^2}(X-x)\)to the next one
\(\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\)

Answer 6

you multiply both sides by y/b^2 and use (1).

Answer 7

Question: Why do you swap X and x , Y and y?

Answer 8

Oh, write the x and y in (3) as capitals i.e. X and Y.

Answer 9

Nope, that is not correct to me. X is in general, x is a particular x-coordinate of a point.. They are not the same

Answer 10

And you didn't use the condition of p^2, which is the most important clue to turn it true.

Answer 11

substitute the x and y values in (1) and you will get the required solution. Just write in paper. See its coming.

Answer 12

And if you have problem, then swap x by X and y by Y.

Answer 13

Yes, I will.
Thanks for the solution. :)

Answer 14

@Loser66 here's the rest part from which p comes

Answer 15

My stupid brain cannot get it!! Sigh!!

Answer 16

Which part?

Answer 17

Everything!!!

Answer 18

lolz. Let me then explain a bit first the theory portion

Answer 19

The time is off now. I have to leave the lab. I will be back when I get home.

Answer 20

See you know how to find tangent right? by the point slope form.

Answer 21

Again, thanks for the solution.

Answer 22

this got too tricky i think it has to be done more easily. @jango_IN_DTOWN