First slide

Equation of line in Straight lines

Question

If p, q, r are distinct, then (q-r)x + (r-p) y + (p-q)=0 and $(q^{3} - r^{3}) x + (r^{3} - p^{3}) y + (p^{3} - q^{3}) = 0$ represents the same line if

Moderate

A

$p + q + r = 0$
B

$p = q = r$
C

$p^{2} + q^{2} + r^{2} = 0$
D

$p^{3} + q^{3} + r^{3} = 0$

Solution

$\frac{q^{3} - r^{3}}{q - r} = \frac{r^{3} - p^{3}}{r - p} = \frac{p^{3} - q^{3}}{p - q}$

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