Home
Class 11
MATHS
Show that |(z -2)/(z - 3)| = 2 represe...

Show that `|(z -2)/(z - 3)| = 2` represents a circle, find its centre and radius.

Text Solution

AI Generated Solution

To show that the equation \(\left|\frac{z - 2}{z - 3}\right| = 2\) represents a circle and to find its center and radius, we will follow these steps: ### Step 1: Rewrite the equation Start with the given equation: \[ \left|\frac{z - 2}{z - 3}\right| = 2 \] This implies: ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise TRUE/FALSE|9 Videos
  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos
  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos
  • BINOMIAL THEOREM

    NCERT EXEMPLAR|Exercise True/False|7 Videos
  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Objective type|13 Videos

Similar Questions

Explore conceptually related problems

If |(z-2)/(z-3)|=2 represents a circle, then find its radius.

Show that the equaion x ^(2) + y ^(2) - 6x + 4y - 36 = 0 represents a circle. Also, find its centre and radius.

Show that the equation x^(2)+y^(2)+x-y=0 represents a circle find its centre and radius.

Show that the equation 3x^(2)+3y^(2)+6x-4y-1=0 represents a circle Find its centre and radius.

Show that the equation 3x^(2)+3y^(2)+12x-18y-11=0 represent a circle.Also find its centre and radius.

If z=2 + t + i sqrt(3-t^2) , where t is real and t^2 lt 3 , show that the modulus of (z+1)/(z-1) is independent of t. Also show that the locus of the points z for different values of t is a circle and finds its centre and radius.

Show that the equation x ^(2) + y ^(2) + 2x + 10 y + 26 = 0 represents a point circle. Also, find its centre.

If Re ((z + 2i)/(z+4))= 0 then z lies on a circle with centre :