The equation of directrix is to the parabola ` 4x ^ 2 - 4x - 2y + 3 = 0 ` will be

Options

A. `2y = 1 `
B. ` 2x = 1 `
C. `2y = 3 `
D. ` 2x = 3 `

Answer

A

Explanation

Given parabola , ` 4x ^ 2 - 4x - 2y + 3= 0 `
` rArr 4 ( x ^ 2 - x ) = 2y - 3 `
` rArr 4 ( x ^ 2 - x + ( 1 ) /( 4 ) - ( 1 )/( 4 )) = 2y - 3 `
` rArr ( x - ( 1 ) /( 2 ) ) ^ 2 = 2y - 2 `
` rArr ( x - (1 ) /(2 ) ) ^ 2 = 2 ( y -1 ) `
Which is of form
` X^ 2 = 4aY `
where , ` X = x - (1 ) / ( 2 ) and Y = y - 1 `
and ` a = (1 )/ ( 2 ) `
` therefore ` Directrix, ` Y + a = 0 `
` rArr y - 1 + ( 1 ) / ( 2 ) = 0 `
` rArr y - ( 1 ) / ( 2 ) = 0 `
` rArr 2y = 1 `