Let e and l are the eccentricity and length of the lactus rectum respectively of the conic described parametrically by x = t 2 + t + 1 , y = t 2 - t + 1 , then the value of e l 2 is equal to

Question

Let e and l are the eccentricity and length of the lactus rectum respectively of the conic described parametrically by x = t 2 + t + 1 , y = t 2 - t + 1 , then the value of e l 2 is equal to,

MARKS App · Accepted Answer

x + y 2 = t 2 + 1 and x - y 2 = t ⇒ x + y - 2 2 = x - y 2 2 ⇒ x - y 2 2 = 2 x + y - 2 2 Comparing it with y 2 = 4 a x , we get, l = 2 and e = 1 ⇒ e l 2 = 1 2 = 0 . 5

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