Let s be the focus of the parabola S : y2 = 4x. A tangent drawn at any point P of the parabola S = 0 intersects the tangent at the vertex at Q, directrix at R, and x- axis at T. 'A' is the point on parabola S= 0 at which tangent drawn meets the directrix at R.
A circle S1 = 0 is described on the line segment AP as diameter and a circle S2 = 0 is described on sP as diameter which meet normal and tangent drawn at P at points B and C respectively. Line joining sB intersects to a line parallel to x- axis and passing through P, at D.
Normal at P meets the axis at G and parabola at E point.
(i) If point P is (t12, 2t1) and E is (t22, 2t2) then –
Text Solution
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Ans.
(i)
Sol. |t| ≥ 2
(ii)
Sol. t (1+ t2)
(iii)
Sol. 5 sq. units
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