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Questions

Statement-1: Equation of a circle on the ends of a
latus rectum of the hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$ as a diameter is $16 x^{2} + 16 y^{2} \pm 160 x + 319 = 0$
Statement-2: Focus of the parabola $y^{2} = 20 x$ coin cides with a focus of the hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$

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60 mins Expert Faculty Ask Questions

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

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detailed solution

Correct option is B

Foci (±5,0), length of the latus rectum =2×94So the equation of a required circle is (x±5)2+y2= 942⇒16x2+y2±10x+25=81 or 16x2+16y2±160x+319=0and statement-1 is true, statement-2 is also true as the focus of y2=20x is (5,0) but does not justify statement-1.

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