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Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :(i) x2 = -8y(ii) x2 = -18y(iii) 3x2 = -16y |
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Answer» The general form of a parabola: x2 = -4ay ….(1) Focus : F(0, -a) Vertex : A(0,0) (at any point A) Equation of the directrix : y – a = 0 Axis: x = 0 Length of latus rectum : 4a (i) x2 = -8y On comparing given equation with (1), we have 4a = 8 => a = 2 Now, Focus : F(0, -2) Vertex : A(0, 0) Equation of the directrix : y – 2 = 0 Axis: x = 0 Length of latus rectum : 4a = 4 x 2 = 8 units (ii) x2 = -18y On comparing given equation with (1), we have 4a = 18 => a = 9/2 Now, Focus : F(0, -9/2) Vertex : A(0, 0) Equation of the directrix : y – 9/2 = 0 or 2y – 9 = 0 Axis: x = 0 Length of latus rectum : 4a = 4 x 9/2 = 18 units (iii) 3x2 = -16y Or x2 = -16/3 y On comparing given equation with (1), we have 4a = 16/3 => a = 4/3 Now, Focus : F(0, -4/3) Vertex : A(0, 0) Equation of the directrix : y – 4/3 = 0 or 3y – 4 = 0 Axis: x = 0 Length of latus rectum : 4a = 4 x 4/3 = 16/3 units |
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