Show that the points (3, -2), (1, 0), (-1, -2) and (1, -4) are co… - Vidyadip

Question

Show that the points $(3, -2), (1, 0), (-1, -2)$ and $(1, -4)$ are concyclic.

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Answer

we have, P = (3, -2), Q = (1,0), R = (-1,-2) and S = (1, -4) let us consider A circle $x^2 + y^2 + 2gx + 2fy + c = 0$ ........ (1) Passes through P, Q & R
$\therefore$ 9 + 4 + 6g - 4f + c = 0 ........ (2) 1 + 0 + 2g - 0 + c = 0 ............ (3) 1 + 4 - 2g - 4f + c = 0 ............ (4) Solving (2), (3) & (4) we get, g = -1, f = 2 & c = 1 from(1) The required equation of ercle is $x^2 + y^2 - 2x + 4y + 1 = 0$ ......... (5) Clearly s = (1, -4) satisfy (5) Thus, P, Q, R & S are concydic

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