Q.

If e1 and e2 are the roots of the equation x2ax+2=0, then match the following.

COLUMN - ICOLUMN - II
(A) If e1 and e2 are the eccentricities of the ellipse and hyperbola, respectively then the values of a are(p) 6
(B) If both e1 & e2 are the eccentricities of the hyperbolas, then values of a are(q) 52
(C) If e1 and e2 are eccentricities of hyperbola and conjugate hyperbola, then values of a are(r) 22
(D) If e1 is the eccentricity of the hyperbola for which there exists infinite points from which perpendicular tangents can be drawn and e2 is the eccentricity of the hyperbola in which no such points exist then the values of a are(s) 5

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a

A-qs; B-q,; C-r; D-pq

b

A-ps; B-qr,; C-r; D-ps

c

A-s; B-qr,; C-s; D-ps

d

A-ps; B-q,; C-r; D-rs

answer is D.

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Detailed Solution

e1,e2 are roots of x2ax+2=0

 A) e1<1<e2, coefficient of x2=1>0f(1)<0

1a+2<0a>3a=5,6

 B) e1>1,e2>1 roots greater than 1

Δ>0,af(1)>0a(α,2)(2,α),a<3a(2,3)

 C) e12+e22=e12e22e1+e222e1e2=e1e22

a28=0a=22

 D) e1>2,e2<2f(2)<0a>22

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