Hyperbola — Mathematics

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Question 1
EasyJEE

Theparametriccoordinatesofapointontherectangularhyperbolaxy=c2are:The parametric coordinates of a point on the rectangular hyperbola xy = c² are:

A. (ct,c/t)(ct, c/t)
B. (ccos⁡t,csin⁡t)(c \cos t, c \sin t)
C. (csec⁡t,ctan⁡t)(c \sec t, c \tan t)
D. (ct², 2ct)
Question 2
MediumJEE

If e and e₁ are the eccentricities of a hyperbola and its conjugate hyperbola respectively, then:

A. 1/e2+1/e12=11/e² + 1/e₁² = 1
B. e2+e12=1e² + e₁² = 1
C. 1/e2−1/e12=11/e² - 1/e₁² = 1
D. e2−e12=1e² - e₁² = 1
Question 3
MediumJEE

Theeccentricityofthehyperbolax2/16−y2/9=1is:The eccentricity of the hyperbola x²/16 - y²/9 = 1 is:

A. 5/45/4
B. 4/34/3
C. 5/35/3
D. √7/4√7 / 4

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