Equation x^3 + 8y^3 + 24xy = 64 represents - Vidyadip

MCQ

Equation $x^3 + 8y^3 + 24xy = 64$ represents

A
Three straight lines
B
One straight line and one circle
✓
One straight line and one point
D
Two straight lines and one point

✓

Answer

Correct option: C.

One straight line and one point

c
$(x)^{3}+(2 y)^{3}+(-4)^{3}=3(x)(2 y)(-4)$

$\Rightarrow \quad x=2 y=-4 \quad \Rightarrow \quad x=-4, y=-2$

i.e. a point $(-4,-2)$

or $x+2 y-4=0$ i.e. a line

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