Straight Lines Test

Result

Straight Lines Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Find the equation of the line passing through the intersection of the lines x + 2y - 3 = 0 and 4x - y + 7 = 0 and which is parallel to y - x + 10 = 0.

A
3x + 3y + 10 = 0

B
- 3x + 3y + 10 = 0

C
- 3x + 3y - 10 = 0

D
None of these

Solution

Let the equation be x + 2y - 3 + k (4x - y + 7) = 0 ............ (i)

i.e., (1 + 4k) x + (2 - k) y + 7k - 3 = 0

i.e., y = [(-1 - 4k)/(2 - k)]x + (3 - 7k)/(2 - k)

Since it is parallel to y - x + 10 = 0 (i.e., y = x - 10), slopes are equal.

So, (- 1 - 4k)/(2 - k) = 1

- 1 - 4k = 2 - k

k = - 1

Substituting this in eq (i), we get:

The required line is x + 2y - 3 + (-1)(4x - y + 7) = 0

i.e. - 3x + 3y - 10 = 0