1.

Find the vertex, focus, axis , latus rectum and directrix of the parabola y^(2)+4x+6y+17=0

Answer»

Solution :Equation of parabola
`y^(2)+4x+6y+17=0`
`RARR""y^(2)+6y+9=-4x-17+9`
`rArr""(y+3)^(2)=-4(x+2)`
`rArr""Y^(2)=-4X`
Comparing with `Y^(2)=-4AX`
4a=4
`rArr""a=1`
Vertex A = (0,0)
`rArr""X=0,Y=0`
`rArr""x+2=0,y+3=0`
`rArr""x=-2,y=-3`
`:.` Co-ordinates of vertex = (-2,-3).
Focus X = -a,Y=0
`rArr""x+2=-1,y+3=0`
`rArr""x=-3,y=-3`
`:.` Co-ordinates of focus = (-3, -3).
Equation of axis Y=0
`rArr""y+3=0`.
Equation of directrix X=a
`rArr""x+2=1`
`rArr""x+1=0`
Length of latus RECTUM = 4a = 4.


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