Question

The condition that the parabolas y^2=4c(x-d) and y^2=4ax have a common normal other than x axis (a>0,c>0 and c>a) is

Answer 1

@ganeshie8

Answer 2

I found this
a/m=-md+c/m

Answer 3

@phi

Answer 4

what's a "common normal" ?

Answer 5

The normal that is common to both the curves!

Answer 6

Options are
A).2a<2c+d
B).2c<2a+d
C).2d<2a+c
D).2d<2c+a

Answer 7

yes, but what is the definition of a normal ?

Answer 8

A line that is perpendicular to tangent.

Answer 9

@ikram002p

Answer 10

@pawanyadav

Answer 11

Suppose a point (x,y)
Find dy/dx for both curve then equate it..

Answer 12

Did u see my equation in the second post ??

Answer 13

What is m there ?

Answer 14

slope of tangent or normal

Answer 15

Wait!! I did wrong..
I equated the equations of common tangent to the curves

Answer 16

I got this now
2am+am^3=2cm+cm^3+md

Answer 17

So you got option A

Answer 18

Oops A only!

Answer 19

Ty

Answer 20

Yes. ..

Answer 21

No ...it should be 2a>2c+d

Answer 22

@pawanyadav

Answer 23

Why..

Answer 24

I got this
2a+am^2=2c+cm^2+d
And if we take the terms to left side we get
2a-2c-d=(c-a)m^2
So 2a>2c+d

Answer 25

Yes , sorry ... I'm just confused in my question... You are right

Answer 26

Okk..np

Answer 27

I'll tag you in my question .if you can help

Answer 28

I replied lol..