2∣z+1∣=∣z−2∣2|z+1|=|z-2|2∣z+1∣=∣z−2∣
2∣x+iy+1∣=∣x+iy−2∣2|x+iy+1|=|x+iy-2|2∣x+iy+1∣=∣x+iy−2∣
22∣(x+1)+iy∣2=∣(x−2)+iy∣22^2|(x+1)+iy|^2=|(x-2)+iy|^222∣(x+1)+iy∣2=∣(x−2)+iy∣2
4((x+1)2+y2)=(x−2)2+y24((x+1)^2+y^2)=(x-2)^2+y^24((x+1)2+y2)=(x−2)2+y2
4x2+8x+4+4y2=x2−4x+4+y24x^2+8x+4+4y^2=x^2-4x+4+y^24x2+8x+4+4y2=x2−4x+4+y2
3x2+12x+3y2=03x^2+12x+3y^2=03x2+12x+3y2=0
x2+4x+y2=0x^2+4x+y^2=0x2+4x+y2=0
(x2+4x+4)+y2=4(x^2+4x+4)+y^2=4(x2+4x+4)+y2=4
(x+2)2+y2=4(x+2)^2+y^2=4(x+2)2+y2=4
Answer: the locus is a circle with center (−2,0)(-2,0)(−2,0) and radius 222 .
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments
Leave a comment