61.Find the equation of the parabola that satisfying the following condition: Vertex at (0,0), focus on the positive x-axis and length of latus rectum
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62.Find the equation of the parabola that satisfying the following condition: Vertex at (0, 0) focus on the negative side of y-axis and latus rectum equal to it.
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63.Find the equation of a parabola that satisfies the given condition: Focus (6, 0), directrix is x = – 6
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64.Find the equation of a parabola that satisfies the given condition: Focus (0 – 3); directrix y = 3
65.Find the co-ordinates of a point on the parabola y2 = l8x, where the ordinate is 3 times the abscissa.
Let the point be ∴ [∵ Ordinate is 3 times the abscissa] lies on the parabola When Hence, the coordinates of the point are (2, 6).
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66.Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of the latus rectum.
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67.
An equilateral triangle is inscribed in the parabola , where one vertex is at the vertex of the parabola. Find (a) the length of the side of the triangle, (b) area of triangle ABC.
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68.If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
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69.LL' is the latus rectum of a parabola, y2 = 4ax, a > 0. Find the co-ordinates of points L and L'.
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70.LL' is the latus rectum of a parabola, x2 = -8y. Find the co-ordinates of points L and L'.
Short Answer Type
, where one vertex is at the vertex of the parabola. Find (a) the length of the side of the triangle, (b) area of triangle ABC.
[∵ Ordinate is 3 times the abscissa]
lies on the parabola
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