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13 14 16 are the questions. ...kindly help....??...comic sections parsbola

13 14 16 are the questions. ...kindly help....??...comic sections parsbola

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1 Answers

Partha Math Expert - askIITians
askIITians Faculty 25 Points
3 years ago
13.The centre of the circle is equidistant from the line y=x and the point (1,0). Thus, its locus is a parabola with directrix as y=x and focus as (1,0). Hence length of latus rectum = 2 x (distance of focus from directrix) = 2 x (1/√2) =√2.

14.The tangents at the end of latus rectum are at 45° to the axis of the parabola. Since the axes are perpendicular, the tangents at the common end of the latus rectum have an angle 0° or 180°. And cot-11 +cot-1(1/2)+cot-1(1/3) = 180°.

16.A and B satisfy the parametric equation t1t2= -4. The line AB is a family of straight lines passing through (4a, 0).

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