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  • If the focus of the parabola is (-2,-1) and the equation of directrix is x+y=3. Then the coordinates of vertex are:Option: 1 (0,3)<div

If the focus of the parabola is (-2,-1) and the equation of directrix is x+y=3. Then the coordinates of vertex are:

Option: 1

(0,3)


Option: 2

(\frac{-1}{2},\frac{1}{2})


Option: 3

(-1,1/2)


Option: 4

(2,-1)


Answers (1)

As we learnt

 

Directrix -

 

The fixed straight line of a conic section.

- wherein

 

 

 The equation of the axis is x-y=\lambda\: \: i.e.\: \: -2-(-1)=\lambda \Rightarrow \lambda = -1

x-y+1=0

V is vertex and S is focus

Point D is the intersection of Directrix and Axis (1, 2)

Thus V can be calculated

V is the midpoint of S and D

Thus \\h=\frac{-2+1}{2}\:\:,\:\:k=\frac{-1+2}{2}\\(h,k)=(\frac{-1}{2},\frac{1}{2})

 

Posted by

Kshitij

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