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Question

The sides of a rhombus ABCD are parallel to the lines, x−y+2=0 and 7x−y+3=0. If the diagonals of the rhombus intersect at P(1,2) and the vertex A (different from the origin) is on the y−axis, then the ordinate of A is

A
74
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B
2
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C
52
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D
72
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Solution

The correct option is C 52
Let the point A be (0,a)
As we know, diagonals of rhombus will be parallel to the bisector of the lines which are parallel to sides of rhombus
So, bisector of the lines xy+2=0 and 7xy+3=0 are
xy+22=±7xy+352
5x5y+10=±(7xy+3)
So, bisectors are 2x+4y7=0 and 12x6y+13=0
Slope of diagonals =12 and 2
As, slope of AP=2a
2a=12 or 2a=2
a=52 or a=0
a=0 can not be possible because vertex A should be different from the origin.
Hence, a=52

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