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  4. If x+y=k is a tangent to the hyperbola x2-2y2=18, then sum of squares of possible values of k is

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Q. If $x+y=k$ is a tangent to the hyperbola $x^{2}-2y^{2}=18,$ then sum of squares of possible values of $k$ is

NTA AbhyasNTA Abhyas 2022

Solution:

$\frac{x^{2}}{18}-\frac{y^{2}}{9}=1$
Equation of Tangent : $y=-x+k$
$\therefore k^2=18(-1-9$
$k=\pm3$