Question

Find the area of the triangle formed by the lines
$y^2-9xy+18x^2=0$ and $y=9$

Answer 1

The sides of the triangle are $y-3x=0$ and $y-6x=0$ and
$y=9$.

Solving in pairs, its vertices are
$(0,0); \left( \dfrac { 3 }{ 2 } ,9 \right) ;\left(
3,9 \right)$

or $\triangle =\dfrac{ 1 }{ 2 }(x_{ 1 }y_{ 2 }-x_{ 2 }y_{
1 })=\dfrac{ 27 }{ 4 }sq.$ units.