Q96 / 150 · MHT CET 2012 · Mathematics

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

  • A
    $-1$
  • B
    1
  • Correct answer
    C
    $-2$
  • D
    2

Solution

If the $(3, \lambda \lambda \lambda \lambda)$ and $(5,6)$ are the conjugate points to the curve $x^{2}+y^{2}=3$, then $\begin{aligned} x_{1} x_{2}+y_{1} y_{2} &=3 \\ \Rightarrow \quad(3)(5)+(\lambda \lambda \lambda \lambda) \cdot(6) &=3 \end{aligned}$ $\Rightarrow \quad 15+6(\lambda \lambda \lambda \lambda)=3$ $\Rightarrow 6(\lambda \lambda \lambda \lambda)=-12$ $\Rightarrow \lambda \lambda \lambda \lambda=-2$

Hence, the correct answer is option: 'C'.

More Circle Questions