AM-1138

Line meeting a curve

A Math · Secondary 4 · Hard · Line meeting a curve

The line with equation

y = 2x - 1

intersects the curve

x^2 - 4xy + y^2 + 10 = 0

at points

P

and

Q

. Find the coordinates of

P

and

Q

.

$P(\sqrt{11/3}, 2\sqrt{11/3}-1),\ Q(-\sqrt{11/3}, -2\sqrt{11/3}-1)$
$P(\sqrt{11/3}, 2\sqrt{11/3}+1),\ Q(-\sqrt{11/3}, -2\sqrt{11/3}+1)$
$P(\sqrt{11/3}, -2\sqrt{11/3}-1),\ Q(-\sqrt{11/3}, 2\sqrt{11/3}-1)$
$P(\sqrt{11/3}, 2\sqrt{11/3}-1),\ Q(-\sqrt{11/3}, 2\sqrt{11/3}-1)$

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