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? 

–19 + 15i


–16 – 22i
6 + 16i
20 – 24 i

Answer 1

it would be option 2

Answer 2

Option B (-16-22i)

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=√((x-h)^2+(y-k)^2)`

`r=√((4-(-6))^2+(26-2)^2)`

`r=√((10)^2+(24)^2)`

`r=√(100+576)`

`r=√(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\\eq676`

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\\eq676`

D) 20 – 24i=(20,-24)

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

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

`(676)+(676)=676`

`1352\\eq676`

Therefore, Option B only satisfy the required equation

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