Hello snigdha Originally Posted by
snigdha Find the equation of a line through (1,3) and forming with the axes a triangle of area 6 square units. (Give three solutions).
Suppose 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.
Grandad