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.

✓

Answer

we have,
P = (3, -2), Q = (1,0), R = (-1,-2) and S = (1, -4)
let us consider A circle x² + y² + 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
x² + y² - 2x + 4y + 1 = 0 ......... (5)
Clearly s = (1, -4) satisfy (5)
Thus,
P, Q, R & S are concydic

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