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Statement-1: If the foci of a hyperbola are at the points (4, 1) and (–6, 1), eccentricity is 5/4 then the length of the transverse axis is 8.Statement-2: Distance between the foci of a hyper bola is equal to the product of its eccentricity and the length of the transverse axis

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a

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

b

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

c

STATEMENT-1 is True, STATEMENT-2 is False

d

STATEMENT-1 is False, STATEMENT-2 is True

answer is A.

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Detailed Solution

Statement-2 is true, as the distance between the foci of x2a2−y2b2=1 is 2ae where 2a is the length of the transverse axis and e is the eccentricityUsing it in statement-1, length of the transverse axis is (4+6)25/4=10×45=8 and thus statement-1 is also true.

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