If the join of ends of the latusrectum of x2-8y subtends an angle - at the vertex of the parabola then cos-

The correct option is D 35 Applying cosine rule cosθ=20+20 642.√(20)√(20)= 242.20= 35 ...

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Standard XII

Mathematics

Rotation Concept

If the join o...

Question

If the join of ends of the latusrectum of $x^{2} = 8 y$ subtends an angle $θ$ at the vertex of the parabola then $cos θ =$

\frac{- 4}{5}

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\frac{- 2}{3}

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\frac{- 3}{5}

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\frac{- 1}{5}

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Solution

The correct option is D $\frac{- 3}{5}$
Applying cosine rule-
$cos θ = \frac{20 + 20 - 64}{2. \sqrt{20} \sqrt{20}} = \frac{- 24}{2.20} = \frac{- 3}{5}$

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Similar questions

Let $P Q$ be a focal chord of $y^{2} = 4 a x$ . The tangents to parabola at $P$ and $Q$ meet at a point lying on the line $y = 2 x + a (a > 0)$ . If the chord $P Q$ subtends an angle $θ$ at the vertex of prabola then $tan θ =$

Q. Let PQ be a focal chord of the parabola

y^{2} = 4 x

. The tangents to the parabola at P and Q meet at a point on
y = 2x + 1.

If PQ subtends an angle

θ

at the vertex of

y^{2} = 4 x

, then

t a n θ

Q. Let

P Q

be a focal chord of the parabola

y^{2} = 4 a x

. The tangents to the parabola at

P

and

Q

meet at a point lying on the line

y = 2 x + a, a > 0

.
If chord

P Q

subtends an angle

θ

at the vertex of

y^{2} = 4 a x

, then tan

θ

is equal to

If cos $θ$ = $\frac{3}{5}$ and cos $ϕ$ = $\frac{4}{5}$ , where $θ$ and $ϕ$ are

positive acute angles, then cos $\frac{θ - ϕ}{2}$ =

Q. If latus rectum of ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{b^{2}} = 1 (0 < b < 4)

subtends angle

2 θ

at farthest vertex s.t

cosec θ = 5

then

e = ?

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If the join of ends of the latusrectum of x2=8y subtends an angle θ at the vertex of the parabola then cosθ=

The correct option is D −35Applying cosine rule-cosθ=20+20−642.√20√20=−242.20=−35

If the join of ends of the latusrectum of $x^{2} = 8 y$ subtends an angle $θ$ at the vertex of the parabola then $cos θ =$

The correct option is D $\frac{- 3}{5}$
Applying cosine rule-
$cos θ = \frac{20 + 20 - 64}{2. \sqrt{20} \sqrt{20}} = \frac{- 24}{2.20} = \frac{- 3}{5}$