a straight line passing through the point (3,1) makes a triangle with the axes. the area of the triangle is 8sq. units. find the equation of two such straight lines.
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Let us say the equation of such a line is
x/a + y/b = 1, here a and b are intercepts on the coordinate axis by the line.
then 1/2* a b = area of triangle = 8 sq units => ab = 16 square units
3/a + 1/b = 1 => 3 b + a = ab = 16
3 b + 16/b = 16
3 b² -16 b + 16 = 0
b = [ 16 +- √(256-192) ] / 6 = 4/3 or 4
a = 12 or 4
hence the two lines are : bx + ay = ab =>
4/3 x + 12 y = 16 => x + 9 y = 12
4 x + 4 y = 16 => x + y = 4
x/a + y/b = 1, here a and b are intercepts on the coordinate axis by the line.
then 1/2* a b = area of triangle = 8 sq units => ab = 16 square units
3/a + 1/b = 1 => 3 b + a = ab = 16
3 b + 16/b = 16
3 b² -16 b + 16 = 0
b = [ 16 +- √(256-192) ] / 6 = 4/3 or 4
a = 12 or 4
hence the two lines are : bx + ay = ab =>
4/3 x + 12 y = 16 => x + 9 y = 12
4 x + 4 y = 16 => x + y = 4
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