If the line x-1 is the directrix of the parabola y2-k x-8-0 then positive value of k isA- 1 - 4B- 8C- 1 - 8D- 4

The correct option is D 4 Equation of parabola isy^2=k (x 8/k )⇒(y 0)^2=k (x 8/k ) ∴Equation of directrix is x 8/k= k/4⇒x=8/k k/4 But given x = 1 is directrix ...

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Byju's Answer

Standard XII

Mathematics

General Equation of Parabola

If the line x...

Question

If the line x = 1 is the directrix of the parabola y² – kx + 8 = 0 then positive value of k is _______

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Solution

The correct option is A
4

$Equation of parabola is y^{2} = k (x - \frac{8}{k}) \Rightarrow (y - 0)^{2} = k (x - \frac{8}{k}) ∴ Equation of directrix is x - \frac{8}{k} = \frac{- k}{4} \Rightarrow x = \frac{8}{k} - \frac{k}{4} But given x = 1 is directrix \Rightarrow 1 = \frac{8}{k} - \frac{k}{4} \Rightarrow k = - 8, 4$

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If the line x = 1 is the directrix of the parabola y2 – kx + 8 = 0 then positive value of k is _______

The correct option is A 4 Equation of parabola isy2=k(x−8k)⇒(y−0)2=k(x−8k)∴Equation of directrix is x−8k=−k4⇒x=8k−k4But given x = 1 is directrix ⇒1=8k−k4⇒k=−8,4

If the line x = 1 is the directrix of the parabola y² – kx + 8 = 0 then positive value of k is _______