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Let V be the vertex and L be the latusrectum of the parabola x 2 = 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) y 2 = x – 2 (b) y 2 = x – 4 (c) y 2 = 2 – x (d) y 2 = 4 – x



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


Grade:10

1 Answers

Amit Saxena
35 Points
7 years ago

(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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