Q7 / 105 · NTA Abhyas (JEE Main) 2020 · Mathematics · Three Dimensional Geometry

If the line $\frac{x - 1}{5} = \frac{y - 3}{2} = \frac{z - 3}{2}$ intersects the curve $x^{2} - y^{2} = k^{2}, z = 0,$ then the value of $2 k$ can be equal to

Correct answer
A
$- 13$
B
$- \frac{13}{2}$
C
$\frac{13}{2}$
D
$\frac{13}{4}$

Solution

Put

z = 0

in the given equation of line

\frac{x - 1}{5} = \frac{y - 3}{2} = - \frac{3}{2}

\Rightarrow x = - \frac{13}{2}, y = 0

So,

{(- \frac{13}{2})}^{2} - 0 = k^{2} \Rightarrow k = \pm \frac{13}{2}

Hence, the correct answer is option: 'A'.

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