Area of the triangle formed by the lines y^2 -9xy + 18x^2 = 0 and… - Vidyadip

MCQ

Area of the triangle formed by the lines $y^2 -9xy + 18x^2 = 0$ and $y = 9$ , is ............ $\mathrm{sq. \,unit}$

A
$27$
B
$13.5$
✓
$6.75$
D
$3.375$

✓

Answer

Correct option: C.

$6.75$

c
Put $y=9$ in given pair of straight lines

$18 x^{2}-81 x+81=0$

$\Rightarrow \quad x=3, \frac{3}{2}$

So, we have three vertices $(0,0),(3,9)$

$\operatorname{and}\left(\frac{3}{2}, 9\right)$

Hence $\Delta=\frac{27}{4}$

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