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# Solution - If an equation hxy + gx + fy + c = 0 represents a pair of lines, then - Pair of Straight Lines - Condition for Parallel Lines

#### Question

If an equation hxy + gx + fy + c = 0 represents a pair of lines, then.........................

(a) fg = ch                       (b) gh = cf

(c) Jh = cg                     (d) hf= - eg

#### Solution

(a)

Consider the general equation in second degree,
a'x 2+2h'xy + b'y2 + 2g'x + 2f'y + c' = 0
The above equation will represent a pair of straight lines if,
a'f'2 + b'g'2 + c'h'2 = 2f'g'h' + a'b'c'....(1)
Here, the given equation is, hxy + gx + fy + c = 0
Thus, comparing the coefficients, we have,
a' = 0, b' = 0, c' = 0, h' =h/2 , g' =g/2 , f' =f/2 , c' = c/2
Substituting the above values in the condition (1),
we have,

(0)(f/2)^2+(0)(g/2)^2+(c)(h/2)^2=2xxf/2xxg/2xxh/2+(0)xx(0)xx(0)

(c)(h/2)^2=2xxf/2xxg/2xxh/2

(ch^2)/4=(fgh)/4

ch^2=fgh

ch=fg [because h!=0]

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March)
Question 1.1.3 | 2 marks
Solution for question: If an equation hxy + gx + fy + c = 0 represents a pair of lines, then concept: Pair of Straight Lines - Condition for Parallel Lines. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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