First slide

Definition of a circle

Question

Four distinct points $(2 k, 3 k), (1, 0), (0, 1)$ and $(0, 0)$ lie on a circle for

Moderate

A

all integral values of k
B

0 < k < l
C

k < 0
D

for two values of k

Solution

The equation of the circle passing through the point (1, 0), (0, 1) and (0, 0) is $x^{2} + y^{2} - x - y = 0$
This passes through $(2 k, 3 k)$
$4 k^{2} + 9 k^{2} - 2 k - 3 k = 0 \Rightarrow k = 0, k = 5 / 13$

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