If ^2 = x^2 + y^2 + 1 2x , then x must be - Vidyadip

MCQ

If ${\sin ^2}\theta = \frac{{{x^2} + {y^2} + 1}}{{2x}}$, then $x$ must be

A
$-3$
B
$-2$
C
$1$
✓
None of these

✓

Answer

Correct option: D.

None of these

d
(d) ${\sin ^2}\theta \le 1$

$\therefore$ $\frac{{{x^2} + {y^2} + 1}}{{2x}} \le 1$

$\Rightarrow$ ${x^2} + {y^2} - 2x + 1 \le 0$.

$\Rightarrow$ ${(x - 1)^2} + {y^2} \le 0$

It is possible, if $x = 1$ and $y = 0$,

$i.e.$, It also depends on value of $y$.

Hence, option $(d)$ is correct.

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