Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaGeneralEasy2 minQB

MathematicsEasyinteger

If the line $x - 1 = 0$ is the directrix of the parabola $y^{2} - k x + 8 = 0$ , then $k (> 0)$ is

Answer:

Solution:

$y^{2} = k x - 8$

$y^{2} = k (x - 8/ K)$

$r (8/ K, 0); 4 a = K$

$a = \frac{K}{4}$

We know that $rz = a$

$\Rightarrow \frac{8}{K} - 1 = \frac{K}{4}$

$\Rightarrow \frac{8}{K} - \frac{K}{4} = 1$

$\Rightarrow 32 - K^{2} = 4 K$

$\Rightarrow K^{2} + 4 K - 32 = 0$

$\Rightarrow K (K + 8) - 4 (K + 8) = 0$

$K = 4$ or $K = - 8$ X

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:General

⏱ 2mℹ️ Source: QB

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