Question

Locus of point of contact of tangents drawn from (0,2) upon a variable ellipse x^2/4 + y^2/b^2=1
0 10 years ago

Answer 1

@ganeshie8

Answer 2

@vishweshshrimali5

Answer 3

First thing first... can you draw the ellipse?

Answer 4

You know the major and minor axes length

Answer 5

Major axis is of length 4 and minor of 2b

Answer 6

Are you sure about the major axis length?

Answer 7

Yup!!

Answer 8

Shouldn't it be 8 ? ;)

Answer 9

a^2=4
Hence 2a=4

Answer 10

Ooops :P Sorry my bad :)

Answer 11

Now, can you draw the complete figure... you know the ellipse and the point (0,2)... try drawing the tangents

Answer 12

all we need is a rough figure to get an idea of what we have to calculate

Answer 13

Okay!

Answer 14

shall we apply pair of tangents equation here??
Bt i think that it's not working here v will be left with b term as well and in the options there is no b as such!

Answer 15

@vishweshshrimali5

Answer 16

I will have to look into it..

Answer 17

Okay!

Answer 18

Now, the equation of the tangent to x^2/a^2 + y^2/b^2 = 1 at P(x1,y1) is x*x1/a^2 + y*y1/b^2 = 1.

Answer 19

(x1,y1) are (0,2)

Answer 20

Sorry no..

Answer 21

I thought u were also writing pair of tangents from that point A (0,2)

Answer 22

Naah :) So, basically we have to find out (x1, y1)

Answer 23

Okk, so we can simply put (0,2) into this equation n we will get an eq of tangent passing through that point on the ellipse at any general point on the ellipse (x1,y1)

Answer 24

I can also use the fact that (0,2) will lie on this tangent as well.. So, if I plug in x = 0 and y = 2, I get:

y1/b^2 = 1

Answer 25

Thus the equation of tangent will become:

x*x1/4 + y = 1

=> x*x1 + 4y = 4

Answer 26

Correct !

Answer 27

Great!! :D

Answer 28

V need to eliminate x from here if we need to find out the locus of (x1,y1)

Answer 29

Yeah...

Answer 30

x^2/4+y^2/b^2=1

Answer 31

Plugging the value of x1 into the ellipse equation we get y1

Answer 32

Great!! And then we can find out the locus ..

Answer 33

Let's see if i got it right or not!!

Answer 34

Okay (y)

Answer 35

Hey! I m getting a term of b also in locus...

Answer 36

uh oh :/

Answer 37

I will look into it tomorrow then.. till then can you check whether what we did till now is correct or not?

Answer 38

Wrong it was at one step of yours!

Answer 39

2k/b^2=1

Answer 40

k ?

Answer 41

I assumed point on ellipse to be (h,k)

Answer 42

Damn!!!!!

Answer 43

Bt that will not eliminate b from our locus equation it was just a calco mistake from your side..

Answer 44

Yeah :/ Well anyways.. will try it again from start tomorrow...

Answer 45

Ok!