Question

Find the co-ordinates of vertex of the parabola whose focus is (0,0) and the directrix is the line 2x +y=1
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Answer 1

Answer:

ANSWER

Focus(0,0)

eq

n

of directrix = 2x−y−1=0

Let A(x,y) be the pt. on the parabola

and AM be the length of the perpendicular

from A to the directrix.

Then,

SA = AM

⇒(SA)

2

=(AM)

2

⇒(x−0)

2

+(y−0)

2

=(

2

2

+(−1)

2

2x−y−1

)

2

⇒x

2

+y

2

=

5

(2x−y−1)

2

⇒5x

2

+5y

2

=4x

2

+y

2

−4xy+1+4x−2y

⇒x

2

+4y

2

+4xy−4x+2y−1=0

Which is the required eq

n

of parabola.

Step-by-step explanation:

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