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 $\displaystyle m$. Then its equation is:

$\displaystyle y-1=m(x-3)$Simplify this, and then find the coordinates of the intercepts. They are:$\displaystyle \left(\frac{m-3}{m},0\right)$ and $\displaystyle (0, 3-m)$Then, using $\displaystyle \tfrac12$ base x height, write down an expression to represent the area of the triangle, and equate this to $\displaystyle \pm 6$. (You need the $\displaystyle \pm$ sign, because you might have negative distances, and hence a negative area.

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

Solve these to find the possible values of $\displaystyle m$, and hence the equations of the lines.

__Spoiler__:

Grandad