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)

Question

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) (A)  (5+√11/6) (B) (2 √5+4/6) (C) (5-√11/6) (D) (2 √5-4/6)

Tardigrade Admin · Accepted Answer

Equation of chord of contact 6 sin θ y=6 cos θ+x-11 Focus =(6,0) 0=6 cos θ+6-11 ⇒ cos θ=(5/6) ⇒ sin θ+ cos θ=(5 ± √11/6)

Q. Consider a parabola $y^{2} = 2 x - 11$ and a point $P (6 cos θ, 6 sin θ), θ \in (0, 2 π)$ . 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)

$\frac{5 + 11}{6}$

$\frac{2 5 + 4}{6}$

$\frac{5 - 11}{6}$

$\frac{2 5 - 4}{6}$

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

Q. Consider a parabola y2=2x−11 and a point P(6cosθ,6sinθ),θ∈(0,2π). 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 ( sinθ +cosθ) is (are)

65+11​​

625​+4​

65−11​​

625​−4​