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If the eccentricity of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(9)=1and(y^(2))/(b^(2))-(x^(2))/(a^(2))=1" are "e_(1)ande_(2)` respectively then prove that :
`(1)/(e_(1)^(2))+(1)/(e_(2)^(2))`

A

1

B

2

C

3

D

4

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The correct Answer is:
A
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If the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1and(y^(2))/(b^(2))-(x^(2))/(a^(2))=1" are "e_(1)ande_(2) respectively then prove that : (1)/(e_(1)^(2))+(1)/(e_(2)^(2))

Find the eccentricity of hyperbola x^(2)-9y^(2)=1 .

Statement- 1 : If 5//3 is the eccentricity of a hyperbola, then the eccentricity of its conjugate hyperbola is 5//4 . Statement- 2 : If e and e' are the eccentricities of hyperbolas (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (x^(2))/(a^(2))-(y^(2))/(b^(2))=-1 respectively, then (1)/(e^(2))+(1)/(e'^(2))=1 .

If e_(1)ande_(2) be the eccentricities of the ellipses (x^(2))/(a^(2))+(4y^(2))/(b^(2))=1and(x^(2))/(a^(2))+(4y^(2))/(b^(2))=1 respectively then prove that 3=4e_(2)^(2)-e_(1)^(2) .

If e and e' are the eccentricities of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (y^(2))/(b^(2))-(x^(2))/(a^(2))=1, then the point ((1)/(e),(1)/(e')) lies on the circle (A) x^(2)+y^(2)=1(B)x^(2)+y^(2)=2(C)x^(2)+y^(2)=3(D)x^(2)+y^(2)=4

If e' is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 (a gt b) , then

If e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (where,a lt b), then

If e is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 (a lt b ) , then ,

TARGET PUBLICATION-CIRCLE AND CONICS -COMPETITIVE THINKING
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