Question

# Area of the triangle formed by the lines y2−9xy+18x2=0 and y=9 is

A

B

C

D

Solution

## The correct option is A The lines represented by y2−9xy+18x2=0 are 6x - y = 0 and 3x - y = 0 and third line is y = 9. Therefore, coordinates of vertices of triangle are given by A(0,0); B(3,9) and c(32,9) Hence, area of △ABC=12 ∣∣ ∣ ∣∣0013913291∣∣ ∣ ∣∣=274sq.units. Aliter: Applying the formula given in the theory part, the required area is  (−9)2√(92)2−1818×1+9×0×1+1×0=8118√814−18        = 8118×32=274sq.units.    Mathematics

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