If the line 2x + 3y = 1 touch the parabola y2 = 4ax at the pointP. Find the focal distance of the point P.
Let point P be (at2, 2at). Then tangent at point P will be
ty = x + at2.
Comparing with given the line 2x + 3y = 1.
So, focal distance of point P is .
The points on the parabola y2 = 36x whose ordinate is three times the abscissa are
The points on the parabola y2 = 12x whose focal distance is 4, are
Axis of the parabola x2 – 4x – 3y + 10 = 0 is
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x – 2 = t2, y = 2t are the parameter equations of the parabola
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‘t1’ and ‘t2’ are two points on the parabola y2 = 4x. If the chord joining them is a normal to the parabola at ‘t1’ then
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Find the equation of the parabola whose focus is (1, 1) and the directrix is x + y + 1 = 0.
Find the angle between the tangents of the parabola y2 = 8x, which are drawn from the point (2, 5).