InterviewSolution
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InterviewSolution
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Find the vertex, focus, directrix, latus rectum, equation of latus rectum, equation of axis and co-ordinates of ends of latus rectum for the following parabola : (i) `y^(2)=20x` , (ii)`y^(2)=-8y` (iii) `x^(2)=16y` , (iv) `x^(2)=-8y` (v) `2x^(2)=3y` , (iv) `3y^(2)+4x=0` |
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Answer» Correct Answer - (i) Vertex (0,0), focus (5,0), directrix x=-5, latus rectum = 20, equation of latus rectum x=5, equation of axis y=0, co-ordinates of the ends of latus rectum (5,10),(5-10). (ii) Vertex (0,0), focus (-3,0), directrix x=3, latus rectum = 12, equation of latus rectum x=-3, equation of axis y=0, co-ordinates of the ends of latus rectum (-3,6),(-3-6). (iii) Vertex (0,0), focus (0,4), directrix x=-4, latus rectum y = 16, equation of latus rectum y=4, equation of axis x=0, co-ordinates of the ends of latus rectum (8,4),(-8-4). (iv) Vertex (0,0), focus (0,-2), directrix x=2, latus rectum = 8, equation of latus rectum y=-2, equation of axis x=0, co-ordinates of the ends of latus rectum (4,-2),(-4,-2). (v) Vertex (0,0), focus `(0,(3)/(8))`, directri x `y=-(3)/(8)`, latus rectum `=(3)/(2)`, equation of latus rectum `y=(3)/(8)`, equation of axis x=0, co-ordinates of the ends of latus rectum `((-3)/(4),(3)/(8)),((3)/(4),(3)/(8))`. (vi) Vertex (0,0) focus `(-(1)/(3),0)`, directrix `x-(1)/(3)`, latus rectum `=(4)/(3)`, equation of latus rectum `x=-(1)/(3)`, equation of directrix y = 0, co-ordinates of the ends of latus rectum `(-(1)/(3),(2)/(3)),(-(1)/(3),-(2)/(3))`. |
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