If $(3, λ)$ and $(5, 6)$ are the conjugate points to the curve $x^{2} + y^{2} = 3$ , then $λ$ is

- 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $- 2$
If the $(3, λ)$ and $(5, 6)$ are the conjugate points to the curve $x^{2} + y^{2} = 3$ , then
$x_{1} x_{2} + y_{1} y_{2} = 3$
$\Rightarrow (3) (5) + (λ) \cdot (6) = 3$
$\Rightarrow 15 + 6 (λ) = 3$
$\Rightarrow 6 (λ) = - 12$
$\Rightarrow λ = - 2$

Suggest Corrections

Similar questions

If the tangents form the point $(λ, 3)$ to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ are at right angles, then $λ$ =

Q. From the point

(λ, 3)

tangents are drawn to

\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1

and are perpendicular to each other then

λ =

Q. The tangent from the point

(λ, 3)

to the ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1

are at right angles then

λ

If the points (–1, 3, 2), (–4, 2, –2) and (5, 5, $λ$ ) are collinear, then $λ$ =

The lines joining the points of intersection of line x + y = 1 and curve $x^{2} + y^{2} - 2 y + λ = 0$ to the origin are perpendicular, then the value of $λ$ will be

Join BYJU'S Learning Program

If (3,λ) and (5,6) are the conjugate points to the curve x2+y2=3, then λ is

The correct option is B −2If the (3,λ) and (5,6) are the conjugate points to the curve x2+y2=3, thenx1x2+y1y2=3⇒(3)(5)+(λ)⋅(6)=3⇒15+6(λ)=3⇒6(λ)=−12⇒λ=−2

If $(3, λ)$ and $(5, 6)$ are the conjugate points to the curve $x^{2} + y^{2} = 3$ , then $λ$ is

The correct option is B $- 2$
If the $(3, λ)$ and $(5, 6)$ are the conjugate points to the curve $x^{2} + y^{2} = 3$ , then
$x_{1} x_{2} + y_{1} y_{2} = 3$
$\Rightarrow (3) (5) + (λ) \cdot (6) = 3$
$\Rightarrow 15 + 6 (λ) = 3$
$\Rightarrow 6 (λ) = - 12$
$\Rightarrow λ = - 2$