Question

Show that there are two lines which pass through the point a(3, 7) and the sum of whose intercept on the co ordinate x is zero. draw the rough sketch of these two lines​

Answer 1

The proof is given below:

We know that equation of the line whose x and y intercepts are a and b is

$\frac{x}{a}+\frac{y}{b}=1$

Since the sum of the intercepts is zero

Therefore,

$a+b=0$

$\implies b=-a$

Thus, the equation of the line becomes

$\frac{x}{a}+\frac{y}{-a}=1$

$\implies x-y=a$

Since this line passes through point (3, 7)

Therefore, this point will satisfy the equation of the line

Thus,

$3-7=a$

$\implies a=-4$

Hence, the equation becomes

$x-y=-4$

or, $y=x+4$

Case II can be when the intercepts on the both axis are itself zero

In this case a = b = 0

Thus, the equation will be of the form

$y=mx$

Since this line will also pass through (3, 7)

Therefore,

$7=m\times 3$

$\implies m=\frac{7}{3}$

Therefore the equation is

$3y=3x$

or, $3y-7x=0$

The sketch is attached.

Hope this answer is helpful.

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