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Let V be the vertex and L be the latusrectum of the parabola x2 = 2y + 4x – 4. Then the equation of the parabola whose vertex is at V, latusrectum is L/2 and axis is perpendicular to the axis of the given parabola.
(a) y2 = x – 2
(b) y2 = x – 4
(c) y2 = 2 – x
(d) y2 = 4 – x
(AC)
Sol. x2 – 4x = 2y – 4
x2 – 4x + 4 = 2y – 4 + 4
(x – 2)2 = 2y
vertex of parabola (2, 0) and length of latusrectum = 2
length of latusrectum of the required parabola = 1
\ equation of the required parabola is
(y – 0)2 = + 1(x – 2)
y2 = x – 2 or y2 = 2 – x
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