Respuesta :
Answer:
Option B (-16-22i)
Step-by-step explanation:
Given : A circle has a center -6+2i and a point is 4+26i
To find : which point is also on the circle
Solution : First we find the radius(r) of the circle with center(x,y)=(-6,2)
and a point (h,k)=(4,26)
Equation of the circle = [tex](x-h)^2+(y-k)^2=r^2[/tex]
where, [tex]r=\sqrt{(x-h)^2+(y-k)^2}[/tex]
[tex]r=\sqrt{(4-(-6))^2+(26-2)^2}[/tex]
[tex]r=\sqrt{(10)^2+(24)^2}[/tex]
[tex]r=\sqrt{100+576}[/tex]
[tex]r=\sqrt{676}[/tex]
[tex]r=26[/tex]
Now we check one by one that which point satisfy the equation
New equation : [tex](x+6)^2+(y-4)^2=676[/tex]
A) point –19 + 15i = (-9,15)
[tex](-19+6)^2+(15-2)^2=676[/tex]
[tex](-13)^2+(13)^2=676[/tex]
[tex](169)+(169)=676[/tex]
[tex]338\neq676[/tex]
B) –16 – 22i =(-16,-22)
[tex](-16+6)^2+(-22-2)^2=676[/tex]
[tex](-10)^2+(-24)^2=676[/tex]
[tex](100)+(576)=676[/tex]
[tex]676=676[/tex]
C) 6 + 16i =(6,16)
[tex](6+6)^2+(16-2)^2=676[/tex]
[tex](12)^2+(14)^2=676[/tex]
[tex](144)+(196)=676[/tex]
[tex]340\neq676[/tex]
D) 20 – 24i=(20,-24)
[tex](20+6)^2+(-24-2)^2=676[/tex]
[tex](26)^2+(-26)^2=676[/tex]
[tex](676)+(676)=676[/tex]
[tex]1352\neq676[/tex]
Therefore, Option B only satisfy the required equation
Hence, Option B (-16-22i) is the answer.
