Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Show that the set of all points such that the difference of their distances from (4, 0) and (– 4, 0) is always equal to 2 represent a hyperbola.

Show that the set of all points such that the difference of their distances from (4, 0) and (– 4, 0) is always equal to 2 represent a hyperbola.

Answers (1)

Let the point be P (x,y)  

According to the question  

Distance of P from (-4,0) -Distance of P from (4,0)=2

\sqrt{\left ( x+4 \right )^{2}+y^{2}}=2+\sqrt{\left ( x-4 \right )^{2}+y^{2}}

Squaring both the sides 

x^{2}+8x+16+y^{2}=4+x^{2}-8x+16+y^{2}+4\sqrt{\left ( x-4 \right )^{2}+y^{2}}

4x-1=\sqrt{\left ( x-4 \right )^{2}+y^{2}}

16x2-8x+1=x2+16-8x+y2

15x2-y2=15

Which is an equation of a hyperbola.

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question