Answered

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 – 24i

Verified Answer :

it would be option 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)

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

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

\((169)+(169)=676\)

\(338 eq676\)

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.

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