1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider a parabola y2=2 x-11 and a point P(6 cos θ, 6 sin θ), θ ∈(0,2 π). Let pair of tangents be drawn to the parabola from the point P. If the corresponding chord of contact is focal chord of the parabola then possible value of ( sin θ + cos θ) is (are)

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Q. Consider a parabola $y^2=2 x-11$ and a point $P(6 \cos \theta, 6 \sin \theta), \theta \in(0,2 \pi)$. Let pair of tangents be drawn to the parabola from the point $P$.
If the corresponding chord of contact is focal chord of the parabola then possible value of ( $\sin \theta$ $+\cos \theta)$ is (are)

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Solution:

Equation of chord of contact $6 \sin \theta y=6 \cos \theta+x-11$
Focus $=(6,0)$
$0=6 \cos \theta+6-11 \Rightarrow \cos \theta=\frac{5}{6} $
$\Rightarrow \sin \theta+\cos \theta=\frac{5 \pm \sqrt{11}}{6}$