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

Find the vertex, focus, directrix, latus rectum, equation of latus rec

1.	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
Answer» 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))`.