Range of values of $k$ for which the point $(k, - 1)$ is exterior to both the parabolas $y^{2} = | x |$ is

(- 1, 0)

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(- 1, 1)

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(0, 1)

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(0, - 1)

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Solution

The correct option is B $(- 1, 1)$
Let $S (x, y) = y^{2} - | x |$
For point $(k, - 1)$ to lie outside the given parabola
$S (k, - 1) > 0$
$\Rightarrow (- 1)^{2} - | k | > 0$
$\Rightarrow | k | < 1$
$\Rightarrow k \in (- 1, 1)$

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Similar questions

λ

(λ, - 1)

y^{2} = | x |

A = [- 1, 1], B = [- 1, 1], C = [0, \infty)

R_{1} = {(x, y) \in A \times B : x^{2} + y^{2} = 1}

R_{2} = {(x, y) \in A \times C : x^{2} + y^{2} = 1}

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