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Class XI Maths Straight Lines 3

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Question 1

Let u ≡ ax +by + a

= 0 and v ≡ bx – ay + b

= 0; a, b∈R be two straight lines. The equations of the bisectors of the angle formed by k₁u – k₂v = 0 and k₁u + k₂v = 0 for non–zero, real k₁ and k₂ are

Question 2

If a + b + c = 0 then the straight line 2ax + 3by + 4c = 0 passes through the fixed point-

Question 3

The equation of the line through the point of intersection of the lines x – y + 4 = 0 and y – 2x – 5 = 0 and passing through the point (3, 2) is -

Question 4

If the sum of the slopes of the lines given by

is four times their product, then c has the value

Question 5

If one of the lines given by 6x²-xy+4cy²=0 is 3x + 4y = 0, then c equals

Question 6

Given the family of lines, a (3x + 4y + 6) + b (x + y + 2) = 0. The line of the family situated at the greatest distance from the point P (2, 3) has equation:

Question 7

Perpendicular bisector of segment PQ is 3x + 4y – 2 = 0. If P is (1, 1) then point Q is -

Question 8

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes then

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