Home
Class 12
MATHS
Show that |(z-2)/(z-3)|=2 represents a c...

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

Text Solution

Verified by Experts

The correct Answer is:
Centre `-=(10//3,0); "Radius" = 2//3`
`|(z-2)/(z-3)| =2`
`rArr |z-2|^(2) = 4|z-3|^(2)`
`rArr |x-2+iy|^(2) = 4|x-3+iy|^(2)`
`rArr(x-2)^(2) + y^(2) = 4[(x-3)^(2) +y^(2)]`
`rArr 3x^(2) + 3y^(2) -(20)/(3)x + (32)/(3) =0`
`rArr x^(2) + y^(2) -(20)/(3)x + (32)/(3) = 0`
`rArr (x-(10)/(3))^(2) + y^(2) = (4)/(9)`
Thus,distance of (x,y) from the point (10/3,0) is 2/3.
So,centre of the circle is (10/3,0) and rasius is 2/3.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.7|6 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.8|11 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise EXERCISE3.5|12 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|101 Videos

Similar Questions

Explore conceptually related problems

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

Find the radius of the circle (xcosalpha+ysinalpha-a)^2+(xsinalpha-ycosalpha-b)^2=k^2,ifalpha varies, the locus of its centre is again a circle. Also, find its centre and radius.

Prove that locus of z is a circle and find its centre and radius if (z-i)/(z-1) is purely imaginary.

If z=x+i y , then the equation |(2z-i)/(z+1)|=m does not represents a circle, when m is (a) 1/2 (b). 1 (c). 2 (d). 3

Find the equation of the circle, the end points of whose diameter are (2, -3) and (-2, 4) . Find its centre and radius.

Find the equation of the circle the end point of whose diameter are (2,-3) and (2,4). Find its centre and radius.

Find the value of a if 2x^(2)+ay^(2)-2x+2y-1=0 represents a circle and also find its radius. (ii) Find the values of a,b if ax^(2)+bxy+3y^(2)-5x+2y-3=0 represents a circle. Also find the radius and centre of the circle. (iii) If x^(2)+y^(2)+2gx+2fy=0 represents a circle with centre (-4,-3) then find g,f and the radius of the circle. (iv) If the circle x^(2)+y^(2)+ax+by-12=0 has the centre at (2,3) then find a ,b and the raidus of the circle. (v) If the circle x^(2)+y^(2)-5x+6y-a=0 has radius 4 , find a

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

Let z_(1),z_(2) and z_(3) be three non-zero complex numbers and z_(1) ne z_(2) . If |{:(abs(z_(1)),abs(z_(2)),abs(z_(3))),(abs(z_(2)),abs(z_(3)),abs(z_(1))),(abs(z_(3)),abs(z_(1)),abs(z_(2))):}|=0 , prove that (i) z_(1),z_(2),z_(3) lie on a circle with the centre at origin. (ii) arg(z_(3)/z_(2))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))^(2) .

Find the equation of the circle with: centre (-2,3) and radius 4.