Suppose $\mathrm{OABC}$ is a rectangle in the $\mathrm{xy}$-plane where o is the origin and $\mathrm{A}, \mathrm{B}$ lie on the parabola $\mathrm{y}=\mathrm{x}^{2}$. Then $\mathrm{C}$ must lie on the curve.

• Correct answer
  A

  $y=x^{2}+2$
• B

  $y=2 x^{2}+1$
• C

  $y=-x^{2}+2$
• D

  $y=-2 x^{2}+1$

Solution

$m_{O A} \times m_{O B}=-1$ $t_{1} t_{2}=-1$ $t_{1}+t_{2}=h$ $K=\left(t_{1}+t_{2}\right)^{2}-2 t_{1} t_{2}$ $K=h^{2}+2 \Rightarrow y=x^{2}+2$

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