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The equation of the line passing through the intersection of x - √3 y + √3 - 1 = 0 and x y–2 = 0 and
making an angle of 150 with the first line is
  • a)
    x–y=0
  • b)
    x–y 1 = 0
  • c)
    y =1
  • d)
    √3 x -y +1 = 0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The equation of the line passing through the intersection of x -&radic...
Y = 5 and 3x + 2y = 10 and perpendicular to the line 2x - y = 3 is:

First, we need to find the intersection point of the two given lines. To do this, we can solve the system of equations:

x - y = 5
3x + 2y = 10

Multiplying the first equation by 2, we get:

2x - 2y = 10

Adding this to the second equation, we eliminate y:

5x = 20

x = 4

Substituting x = 4 into the first equation, we get:

4 - y = 5

y = -1

So the intersection point is (4, -1).

To find the slope of the line perpendicular to 2x - y = 3, we can rearrange this equation into slope-intercept form:

y = 2x - 3

The slope of this line is 2. The slope of any line perpendicular to this line is the negative reciprocal of 2, which is -1/2.

So the equation of the line we want is:

y - (-1) = (-1/2)(x - 4)

Simplifying:

y + 1 = (-1/2)x + 2

y = (-1/2)x + 1

Therefore, the equation of the line passing through the intersection of x - y = 5 and 3x + 2y = 10 and perpendicular to the line 2x - y = 3 is y = (-1/2)x + 1.
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The equation of the line passing through the intersection of x -√3 y +√3 - 1 = 0and x y–2 = 0 andmaking an angle of 150with the first line isa)x–y=0b)x–y 1 = 0c)y =1d)√3 x -y +1 = 0Correct answer is option 'A'. Can you explain this answer?
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