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in Two Dimensional Analytical Geometry by (46.9k points)
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If one of the lines given by 6x2 – x + 4x2 = 0 is 3x + 4y = 0, then c equals to …

(a) -3 

(b) -1 

(c) 3 

(d) 1

1 Answer

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Best answer

(a) -3

6x2 – xy + 4cy2 = 0, 3x + 4y = 0 

The other line may be (2x + by) 

(3x + 4y) (2x + by) = 6x2 – xy + 4cy2 

6x2 + 3xby + 8xy + 4by2 = 6x2 – xy + 4cy2 

6x2 + xy (3b + 8) + 4by2 = 6x2 – xy + 4cy2 paring, 3b + 8 = -1 

3b = -9 ⇒ b = -3 

4b = 4c ⇒ 4(-3) = 4c 

-12 = 4c ⇒ c = -3

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