Q.
The straight lines represented by (y−mx)2=a2(1+m2) and (y−nx)2=a2(1+n2) form a
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a
rectangle
b
rhombus
c
trapezium
d
None of these
answer is B.
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Detailed Solution
The straight lines represented by (y−mx)2=a2(1+m2) are y−mx=±a1+m2i.e.,y−mx=a1+m2 (1) and y−mx=−a1+m2(2) Similarly, the straight lines represented by (y−nx)2=a2(1+n2) are y−nx=a1+n2(3) and y−nx=−a1+n2 (4) Since the lines (1) and (2) are parallel, the distance between them is |a1+m2+a1+m21+m2|=|2a|Similarly, the lines (3) and (4) are parallel lines and the distance between them is |2a|.Since the distance between parallel lines are the same, the four lines form a rhombus.
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