Home
Class 12
MATHS
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`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the vertex and focus of a parabola are (3,3) and (-3,3) respectively, then its equation is

If the focus and the vertex of a parabola are (2,3) and (-1,1) respectively, then the directrix is :

If the focus and vertex of a parabola are the points (0, 2) and (0, 4), respectively, then find the equation

If the focus and vertex of a parabola are the points (0, 2) and (0, 4), respectively, then find the equation

If the focus of a parabola is (-2,1) and the directrix has the equation x+y=3 then its vertex is a. (0,3) b. (-1,1/2) c. (-1,2) d. (2,-1)

If the points (0,4)a n d(0,2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.

If the points (0,4)a n d(0,2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.

Find the equation of the parabola with focus (-3,0) and the equation of the directrix is x = 3.

The focus and directrix of a parabola are (1, 2) and x + 2y + 9 = 0 then equation of tangent at vertex is

Find the equation of the parabola whose focus is (-1,-2) and the equation of the directrix is given by 4x-3y+2=0 . Also find the equation of the axis.