If e1 and e2 are the roots of the equation x2−ax+2=0, then match the following COLUM N-I COLUM N-IIA)If e1 and e2 are the eccentricities of the ellipse and hyperbola, respectively then the value of a areP)6B)If the both e1 and e2 are the eccentricities of the hyperbolas then value of a areQ)5/2C)If e1 and e2 are the eccentricities of Hyperbola and conjugate hyperbola, then the value of a areR)22D)If e1 the eccentricities 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 areS)5

e1+e2=a,e1e2=2A) b2−4ac>0⇒a2−4(2)>0⇒a2>8B)f(1)>0 ⇒1-a+2>0⇒a<3C)e12+e22=e12e22⇒(e1+e2)2=2e1e2+e12e22 ⇒a2=8⇒a=22

If e1 and e2 are the roots of the equation x2−ax+2=0, then match the following COLUM N-I COLUM N-IIA)If e1 and e2 are the eccentricities of the ellipse and hyperbola, respectively then the value of a areP)6B)If the both e1 and e2 are the eccentricities of the hyperbolas then value of a areQ)5/2C)If e1 and e2 are the eccentricities of Hyperbola and conjugate hyperbola, then the value of a areR)22D)If e1 the eccentricities 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 areS)5

e1+e2=a,e1e2=2A) b2−4ac>0⇒a2−4(2)>0⇒a2>8B)f(1)>0 ⇒1-a+2>0⇒a<3C)e12+e22=e12e22⇒(e1+e2)2=2e1e2+e12e22 ⇒a2=8⇒a=22

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If e₁ and e₂ are the roots of the equation $x^{2} - ax + 2 = 0$ , then match the following

COLUM N-I COLUM N-II
A) If e₁ and e₂ are the eccentricities of the ellipse and hyperbola, respectively then the value of a are P) 6
B) If the both e₁ and e₂ are the eccentricities of the hyperbolas then value of a are Q) 5/2
C) If e₁ and e₂are the eccentricities of Hyperbola and conjugate hyperbola, then the value of a are R) $2 \sqrt{2}$
D) If e₁ the eccentricities 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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$A \to Q R, B \to P S, C \to R P, D \to R S$

$A \to P S, B \to Q R, C \to R, D \to P S$

$A \to R S, B \to S P, C \to P R, D \to Q S$

$A \to R, B \to P Q, C \to P, D \to P S$

answer is B.

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Detailed Solution

$e_{1} + e_{2} = a, e_{1} e_{2} = 2$
A) $b^{2} - 4 ac > 0 \Rightarrow a^{2} - 4 (2) > 0 \Rightarrow a^{2} > 8$
$B) f (1) > 0 \Rightarrow 1 - a + 2 > 0 \Rightarrow a < 3$
$C) e_{1}^{2} + e_{2}^{2} = e_{1}^{2} e_{2}^{2} \Rightarrow {(e_{1} + e_{2})}^{2} = 2 e_{1} e_{2} + e_{1}^{2} e_{2}^{2} \Rightarrow a^{2} = 8 \Rightarrow a = 2 \sqrt{2}$

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