First slide

Equation of line in Straight lines

Question

The y-axis and the lines $(a^{5} - 2 a^{3}) x + (a + 2) y + 3 a = 0$ and $(a^{5} - 3 a^{2}) x + 4 y + a - 2 = 0$ are concurrent for

Moderate

A

Two values of a
B

Three values of a
C

Five values of a
D

no value of a

Solution

Let the lines intersect at the point k then
$(a + 2) k + 3 a = 0$ and $4 k + a - 2 = 0$
$\Rightarrow \frac{3 a}{a + 2} = \frac{a - 2}{4} \Rightarrow a^{2} - 12 a + 4 = 0$
which gives us two values of a

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