QJEEM14Ma4139: JEE Main 2014 Mathematics - Class 11 JEEM14Ma4139 Solution: Let a , b , c and d be non-zero numbers. If the point of…

Question

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Let

a, b, c

and

d

be non-zero numbers. If the point of intersection of the lines

4 a x + 2 a y + c = 0

and

5 b x + 2 b y + d = 0

lies in the fourth quadrant and is equidistant from the two axes then :

Accepted Answer

Since the point of intersection lies on fourth quadrant and equidistant from the two axes,

i.e., let the point be (k, $-$ k) and this point satisfies the two equations of the given lines.

$∴$ 4ak $-$ 2ak + c = 0 ......... (1)

and 5bk $-$ 2bk + d = 0 ..... (2)

From (1) we get, $k = \frac{- c}{2 a}$

Putting the value of k in (2) we get,

$5 b (- \frac{c}{2 a}) - 2 b (- \frac{c}{2 a}) + d = 0$

or, $- \frac{5 b c}{2 a} + \frac{2 b c}{2 a} + d = 0$ or, $- \frac{3 b c}{2 a} + d = 0$

or, $- 3 b c + 2 a d = 0$ or, $3 b c - 2 a d = 0$

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