Find the equation of a line through (1,3) and forming with the axes a triangle of area 6 square units. (Give three solutions).

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- Feb 3rd 2010, 02:04 AMsnigdhaEquation of a line (Coordinate geometry)
Find the equation of a line through (1,3) and forming with the axes a triangle of area 6 square units. (Give three solutions).

- Feb 3rd 2010, 02:53 AMGrandad
Hello snigdhaSuppose the line has gradient . Then its equation is:

andThen, using base x height, write down an expression to represent the area of the triangle, and equate this to . (You need the sign, because you might have negative distances, and hence a negative area.

Re-write this as a pair of quadratic equations in (one equation for each of the two possible signs.)

Solve these to find the possible values of , and hence the equations of the lines.

__Spoiler__:

Grandad