Maths-
General
Easy
Question
The angle between the line 2x + y + 1 =0 and x + ky + 5 = 0 is 90° then k = _______
- 1
- 2
- -2
- -1
Hint:
We are given two lines. The angle between the lines is 90°. It means they are perpendicular. We have to find the value of k. We will find the slopes of the lines using slope intercept form. Then, we will use the property of slope of perpendicular lines.
The correct answer is: -2
The given lines are 2x + y + 1 = 0 and x + ky + 5 = 0
We will arrange the equations in slope intercept form.
If m is the slope of line and b is the x-intercept made by the line. Then, the equation of line using slope-intercept form is x = my + b
2x + y + 1 = 0
2x = - y – 1
x = -
y –
x + ky + 5 = 0
x = -ky – 5
So, the slopes of the lines are - and -k
The product of slopes of perpendicular lines is -1
-x -k = -1
K = - 2
The value of k for which the given lines are perpendicular is -2
For such questions, we should know the properties of perpendicular lines. We should know how to find the slopes too.
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