Answered

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Find an equation for the parabola that has its vertex at the origin and satisfies the given condition. Directrix y=1/2

Sagot :

Required equation of the parabola with origin as its vertex and directrix  

y = 1/2 is equal to x² = -2y.

As given in the question,

Let vertex of the parabola be ( h, k )

Vertex of the given parabola be at origin

⇒ ( h , k ) = ( 0 , 0 )

Directrix is y =1/2 above the vertex.

Focus is ( 0, -1/2)

Equation of the parabola is given by

Distance between focus to the vertex = distance between vertex to the directrix

( y - (1/2) )² = ( x - 0)² +  ( y - (-1/2) )²

⇒ y² - y + 1/4 = x² + y² + y + 1/4

⇒ -y = x² + y

⇒x² = -y - y

⇒ x² = -2y

Therefore, the equation of the parabola with vertex at origin and directrix y =1/2 is equal to x² = -2y .

Learn more about parabola here

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