First slide

Pair of straight lines

Question

The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arthemetic mean and geometric mean of 4 and 9 is

Moderate

A

$12 x^{2} - 13 x y + 2 y^{2} = 0$
B

$12 x^{2} + 13 x y + 2 y^{2} = 0$
C

$12 x^{2} - 15 x y + 2 y^{2} = 0$
D

$12 x^{2} + 15 x y - 2 y^{2} = 0$

Solution

$m_{1} + m_{2} = \frac{4 + 9}{2} = \frac{13}{2}, m_{1} m_{2} = \sqrt{4.9} = 6$
$y^{2} - (m_{1} + m_{2}) x y + m_{1} m_{2} x^{2} = 0$
$2 y^{2} - 13 x y + 12 x^{2} = 0$

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