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The equation 9x^3 + 9x^2y - 45x^2 = 4y^3 + 4xy^2 - 20y^2 represent three straight lines, two of which passes through origin. Then find the area of the triangle formed by these lines .

The equation 9x^3 + 9x^2y - 45x^2 = 4y^3 + 4xy^2 - 20y^2 represent three straight lines, two of which passes through origin. Then find the area of the triangle formed by these lines .

Grade:11

2 Answers

Lucky
27 Points
3 years ago
9x^3+ 9x^2y -45x^2-4y^3-4xy^2+20y^2 =0 9x^2(x+y-5) - 4y^2(x+y-5) =0 (9x^2-4y^2) (x+y-5) =0 (3x+2y)(3x-2y)(x+y-5)=0 So equation are 3x +2y=0, 3x-2y=0,x+y-5=0 On solving these equation you will apply the formula for calculating area of triangle from three given points. My answer is 30 sq. units.
Arun
25763 Points
3 years ago
9x^3+ 9x^2y -45x^2-4y^3-4xy^2+20y^2 =0 9x^2(x+y-5) - 4y^2(x+y-5) =0 (9x^2-4y^2) (x+y-5) =0 (3x+2y)(3x-2y)(x+y-5)=0 So equation are 3x +2y=0, 3x-2y=0,x+y-5=0 On solving these equation you will apply the formula for calculating area of triangle from three given points.

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