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Q.

The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of 4 and 9 is

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a

12x2+15xy−2y2=0

b

12x2−15xy+2y2=0

c

12x2−13xy+2y2=0

d

12x2−15xy-2y2=0

answer is A.

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Detailed Solution

y2−m1+m2xy+m1m2x2=0

arthemetic mean :

 ⇒4+92=−2hb ⇒−2hb=132

Geometric mean=4(9)=6⇒ab=6

⇒y2−132xy+6x2=0 ⇒2y2−13xy+12x2=0

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