Question

A circle has center at –6 + 2i and a point on the circle at 4 + 26i. Which of the following points is also on the circle? 

Answer 1

It would be option 2

Answer 2

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 = $(x-h)^2+(y-k)^2=r^2$

where, $r=\sqrt{(x-h)^2+(y-k)^2}$

$r=\sqrt{(4-(-6))^2+(26-2)^2}$

$r=\sqrt{(10)^2+(24)^2}$

$r=\sqrt{100+576}$

$r=\sqrt{676}$

$r=26$

Now we check one by one that which point satisfy the equation

New equation : $(x+6)^2+(y-4)^2=676$

A) point –19 + 15i  = (-9,15)

$(-19+6)^2+(15-2)^2=676$

$(-13)^2+(13)^2=676$

$(169)+(169)=676$

$338\neq676$

B) –16 – 22i  =(-16,-22)

$(-16+6)^2+(-22-2)^2=676$

$(-10)^2+(-24)^2=676$

$(100)+(576)=676$

$676=676$

C) 6 + 16i  =(6,16)

$(6+6)^2+(16-2)^2=676$

$(12)^2+(14)^2=676$

$(144)+(196)=676$

$340\neq676$

D) 20 – 24i=(20,-24)

$(20+6)^2+(-24-2)^2=676$

$(26)^2+(-26)^2=676$

$(676)+(676)=676$

$1352\neq676$

Therefore, Option B only satisfy the required equation

Hence, Option B (-16-22i) is the answer.