यदि एक अतिपरवलय तथा उसके संयुग्मी अतिपरवलय की उत्केन्द्रताएँ e और e' हों, तो सिद्ध कीजिए
`(1)/(e^(2))+(1)/(e'^(2))=1`

If e and e' the eccentricities of a hyperbola and its conjugate,prove that (1)/(e^(2))+(1)/(e^(2))=1

int_(1)^(2)((1)/(x)-(1)/(x^(2)))e^(x)dx=e((e)/(2)-1)

int_(1)^(2)((1)/(x)-(1)/(x^(2)))e^(x)dx=e((e)/(2)-1)

If e and e^(prime) are eccentricities of a hyperbola its conjugate, then (1)/(e^(2))+(1)/((e^(1))^(2))=

If e_1 and e_2 are the eccentricities of a hyperbola and its conjugate then prove that (1)/(e_1^2)+(1)/(e_2^2)=1 .

If e_1, e_2 , are the eccentricities of a hyperbola, its conjugate hyperbola, prove that (1)/(e_1^2)+(1)/(e_2^2)=1 .

Prove that (tan^(-1)1/e)^2+(2e)/((e^2+1)<(tan^(-1)e)^2+2/(sqrt(e^2+1))

if cos (1-i) = a+ib, where a , b in R and i = sqrt(-1) , then a. a = (1)/(2)(e-(1)/(e))cos 1, b = (1)/(2)(e+(1)/(e))sin 1 b. a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1 c. a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e+(1)/(e))sin 1 d. a=(1)/(2)(e-(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1

When the tangent to the curve y=xlogx is parallel to the chord joining the points (1, 0) and (e ,\ e) , the value of x is e^(1//1-e) (b) e^((e-1)(2e-1)) (c) e^((2e-1)/(e-1)) (d) (e-1)/e