Let a circle C in complex plane pass through the points z 1 = 3 + 4 i , z 2 = 4 + 3 i and z 3 = 5 i . If z…

Let a circle C in complex plane pass through the points z1=3+4i,z2=4+3i and z3=5i. If z≠z1 is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then argz is equal to
  1. tan-1247-π
  2. tan-125-π
  3. tan-13-π
  4. tan-134-π

Solution

z1≡A≡3,4, z2≡B≡4,3, z3≡C≡0,5

and z≡P≡x,y

Slope of BC=3-54-0=-12

Slope of AP=2

Now, equation of AP is y-4=2x-3

⇒y=2x-1

Since P lies on circle x2+y2=25

⇒x2+2x-12=25

⇒x=-75 and y=-245

⇒arg(z)=tan-1247-π

Asked in: JEE Main 2022 (25 Jun Shift 1)

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