Find the vertex, co-ordinates of focus, axis , directrix and latus rectum of the following parabolas. (i) y^(2)-6x-4y-11=0 (ii) (x+2)^(2)=2(y+3) (iii) y^(2)=4(x+1) (iv) (y+3)^(2)=4(x-1) (v) x^(2)=2x+2y (vi) 4y^(2)-6x-8y-5=0

Find the vertex, co-ordinates of focus, axis , directrix and latus rec

1.	Find the vertex, co-ordinates of focus, axis , directrix and latus rectum of the following parabolas. (i) y^(2)-6x-4y-11=0 (ii) (x+2)^(2)=2(y+3) (iii) y^(2)=4(x+1) (iv) (y+3)^(2)=4(x-1) (v) x^(2)=2x+2y (vi) 4y^(2)-6x-8y-5=0
Answer» Answer :(i) Vertex `(-(5)/(2),2)`, focus, (-1,2), axis y2=0, equation of directrix x+4=0, latus rectum = (ii) Vertex (-2,-3), focus `(-2,-(5)/(2))`, axis x+2=0, equation of directrix 2y+7=0, latus rectum = 2 (III) Vertex (-1,0), focus (0,0) axis y=0, equation of directrix x+2=0, latus rectum = 2 (iv) Vertex (1,-3), focus (2,-3), axis y+3=0, equation of directrix x=0, latus rectum = 4 (V) Vertex `(1,-(1)/(2))`, focus (1,0), axis x-1=0, equation of directrix y+1=0, latus rectum = 2 (vi) Vertex `(-(3)/(2),1)`, focus `(-(9)/(8),1)`, axis y-1=0, equation of `x=-(15)/(8)`, latus rectum `=(3)/(2)`