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vertex and focus of a parabola are (-1,1...

vertex and focus of a parabola are (-1,1) and (2,3) respectively. find the equation of the directrix.

A

`3x+2y+14=0`

B

`3x+2y-25=0`

C

`2x-3y+10=0`

D

`x-y+5=0`

Text Solution

Verified by Experts

The correct Answer is:
A

As we know that, vertex is the mid-point of the perpendicular drop from the focus of the directrix.
`(alpha+2)/(2) = -1 rArr alpha +2 = -2 rArr alpha = -4`
`(beta +3)/(2) = 1 rArr beta = 2-3= -1`
Slope of axis of the parabola `=(3-beta)/(2-alpha) = (3+1)/(2+4) = (2)/(3)`
Slope of the directrix `=- (3)/(2)`
Equation of directrix is
`y+1= -(3)/(2) (x+4)`
`2y+2= -3x-12`
`3x+2y+14=0`
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