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

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).

Approved