The equation of the line which makes right an | vedclass

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Question

(a) If the line is $\frac{x}{a} + \frac{y}{b} = 1$, then the intercepts on the axes are $a$ and $b$.

Therefore the area is $\frac{1}{2}|a 	imes b|

Vedclass · Accepted Answer

$\frac{x}{4} + \frac{y}{3} = \pm \;1$

Vedclass · Answer

(a) If the line is $\frac{x}{a} + \frac{y}{b} = 1$, then the intercepts on the axes are $a$ and $b$.

Therefore the area is $\frac{1}{2}|a 	imes b| = 6 \Rightarrow |ab| = 12$ &hellip;..$(i)$

and hypotenuse is $5$, therefore ${a^2} + {b^2} = 25$ &hellip;..$(ii)$

On solving $(i)$ and $(ii)$, we get

$a = \pm 4$or $ \pm 3$and $b = \pm 3$or $ \pm 4$

Hence equation of line is $ \pm \frac{x}{4} \pm \frac{y}{3} = 1$or $ \pm \frac{x}{3} \pm \frac{y}{4} = 1$.

Trick: Check with options. Obviously, the line $\frac{x}{4} + \frac{y}{3} = \pm 1$ satisfies both the conditions.

The equation of the line which makes right angled triangle with axes whose area is $6$ sq. units and whose hypotenuse is of $5$ units, is

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