Question

what is the equation of the lines which cuts off an intercept -1 from y axis are equally inclined to the axes are
(Options):
i) x-y+1=0,x+y+1=0
ii) x-y-1=0,x+y-1=0
iii) x-y-1=0,x+y+1=0
iv) None of these​

Answer 1

Answer:

None of these.

Explanation:

The question states that the y-intercept of both the lines is -1.

Therefore, the general equation of line,

$ax + by + c = 0$

From which we derive the slope-intercept form of the line,

$y = (-\frac{a}{b})x + ( -\frac{c}{b})$

Where -(a/b) is the slope of the line and -(c/b) is the y-intercept.

Let the equations of both the lines be,

$a_1x + b_1y + c_1 = 0\\a_2x + b_2y + c_2 = 0$

Given that the y-intercept of both the lines is -1.

$c_1 = c_2 = -1$

This property is found in option (ii).

Now, it is given that both the lines are equally inclined to the axes. Hence, they have equal slopes.

$- \frac{a_1}{b_1} = - \frac{a_2}{b_2}$

The above property is seen in none of the options.

Hence, no option satisifies the given conditions.

Answer 2

Answer:

Explanation:

None of these.

Explanation:

The question states that the y-intercept of both the lines is -1.

Therefore, the general equation of line,

From which we derive the slope-intercept form of the line,

Where -(a/b) is the slope of the line and -(c/b) is the y-intercept.

Let the equations of both the lines be,

Given that the y-intercept of both the lines is -1.

This property is found in option (ii).

Now, it is given that both the lines are equally inclined to the axes. Hence, they have equal slopes.

The above property is seen in none of the options.

Hence, no option satisifies the given conditions.