[(x, y) satisfies 6y - 4x ...] Find the set of all points (x, y) such that the area of the triangle with vertices (0, 0), (6, 4) an

For Competitive Exams

Find the set of all points (x, y) such that the area of the triangle with vertices (0, 0), (6, 4) and (x, y) is 4?

(x, y) lies on the circle (y - 6)2 + (x - 4)2 = 16

(x, y) satisfies 6y - 4x = 8 or 6y - 4x = -8

(x, y) satisfies 6y - 4x = 4 or 6y - 4x = -4

(x, y) satisfies 6y - 4x = 8

Explanation:

Area of a triangle if one of the point is (0, 0) = 12|(x1y2-x2y1)|12|(x1y2-x2y1)|

=> 12|(6 × y - 4 × x)|12|(6 × y-4 × x)| = 4 = 4

=>6y - 4x = 8

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