Home
Class 12
MATHS
What do the {z:|z-a|+|z+a|=2c} "where" |...

What do the `{z:|z-a|+|z+a|=2c} "where" |a|lt c` represent?

Text Solution

Verified by Experts

`{z:|z-a|+|z+a\=2e}`
`"where " |a|lt`
` Here z is a complex number .
Let `z=x=iy.`
`:.(xy)` is the point corresponding the complex number z.
'a' and '-a' be two fixed points.
`:.`Eqn.(1) implies that the sum of the distancer of the point (x,y) from two points a' and '-a` is constant i.e.2c
`:.` The locat is an ellipse.
Promotional Banner

Topper's Solved these Questions

  • AREA UNDER PLANE CURVES (APPLICATION OF DEFINITE INTEGRALS)

    MBD PUBLICATION|Exercise QUESTION BANK|16 Videos
  • CONIC SECTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|179 Videos

Similar Questions

Explore conceptually related problems

What do the {z:|z-a|-|z+a|=c} represent?

What do A, B ,C and D represent ?

On a logarithmic scale, the species area relationship is a straight line described by the equation log S = log C + Z log A. What does S, C, Z and A represent in the given equation? Select the correct answer from the codes given below. {:("Species richness" ,=,1),("Slope of the line",= ,2),("Y-intercept",=,3),("Area",=,4):} a) 1 2 3 4 C S Z A b) 1 2 3 4 S Z C A c) 1 2 3 4 Z S C A d) 1 2 3 4 A C S Z

What do A , B and C represent in the diagram :

Given the equations x=cy+bz, y=az+cx and z=bx+ay where x,y and z are not all zero, prove that a^2+b^2+c^2+2abc=1 by determinant method.

Let CandR denote the set of all complex numbers and all real numbers, respectively. Then, show that f: C rarr R is given by f(z)=|z|, AA z in C , is neither one-one nor onto.

A line with direction ratios lt2,1,2gt meets each of the lines x=y+a=z and x+a=2y=2z. Find the co-ordinates of the points of intersection.