If the lines represented by the equation 9x²-24xy 16y 0 makes angles
Answers
Answer:
Equations of parallel lines will be in the form
a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0
Distance between parallel line
= |c1 - c2|/√(a2 + b2)
(i) Two straight lines represented by the equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 are
parallel if
a/h = h/b = g/f or bg2 = af2
(ii) If ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents a pair of parallel straight lines, then the distance between them is
How to Find Distance Between Two Parallel Lines - Practice questions
Question 1 :
Show that the equation 9x2 − 24xy + 16y2 − 12x + 16y − 12 = 0 represents a pair of parallel lines. Find the distance between them.
Solution :
9x2 − 24xy + 16y2 − 12x + 16y − 12 = 0
a = 9, 2h = -24 ==> h = -12, b = 16, g = -6, f = 8, c = -12
If a pair of straight line is parallel, then it must satisfy the condition given below.
bg2 = af2
16(-6)2 = 9(8)2
576 = 576
Hence the given pair of straight lines is parallel.
Distance between parallel lines
= 2 √(36 - 9(-12))/9(9+16)
= 2 √(36 + 108))/9(25)
= 2 √[144/9(25)]
= 2 [12/3(5)]
= 8/5