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Question 32 of 47

Q.The equation of directrix of the parabola y2=−xy^2 = -x is :

(a) x−4=0x-4=0
(b) 4x+1=04x+1=0
(c) x+4=0x+4=0
(d) 4x−1=04x-1=0
Puducherry TnboardTamil Nadu HSC First Year (DGE) Commerce Board 2023MCQ· 1mImportance★★★★★
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For y2=−xy^2 = -x we get a=14a = \tfrac14; a left-opening parabola has directrix x=ax = a, giving 4x−1=04x - 1 = 0 (option d).

The standard left-opening parabola is

y2=−4ax,y^2 = -4ax,

with vertex at the origin, focus at (−a,0)(-a, 0) and directrix x=ax = a.

Compare with y2=−xy^2 = -x:

4a=1  ⇒  a=14.4a = 1 \;\Rightarrow\; a = \frac{1}{4}.

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