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Q.

Statement-1: The locus of the point of intersection of the tangents that are at right angles to the hyperbola x236-y216=1 is the circle x2+y2=52Statement-2: Perpendicular tangents to the hyperbola x2a2-y2b2=1 interest on the director circle  x2+y2=a2-b2a2>b2 of the hyperbola.

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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 D.

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Detailed Solution

Equation of a tangent to the hyperbola is y = mx+a2m2-b2 and the equation of the tangent perpendicular to it is y=-1mx+a2m2-b2.Eliminating m we get the required locus as (y-mx)2 +(x+my)2=a2m2-b2+a2-b2m2⇒x2+y2=a2-b2 and the statement-2 is true using which statement-1 is false.
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