The acute angle formed between the lines joining the origin to th… - Vidyadip

MCQ

The acute angle formed between the lines joining the origin to the points of intersection of the curve $x^2+y^2-2 x-1=0$ and the line $x+y=1$ is

A
$\tan ^{-1}\left(-\frac{1}{2}\right)$
✓
$\tan ^{-1} 2$
C
$\tan ^{-1} \frac{1}{2}$
D
$60^{\circ}$

✓

Answer

Correct option: B.

$\tan ^{-1} 2$

(B) Given equation of pair of lines is
$x^2+y^2-2 x-1=0$ ...(i)
$x+y=1$ intersects the above pair of lines
$\therefore$ It satisfies equation (i)
$\therefore \quad x^2+y^2-2 x(x+y)-(x+y)^2=0$
$\Rightarrow 2 x^2+4 x y=0 \Rightarrow x^2+2 x y=0$
$\therefore \quad a=1, b=0, h=1$
$\therefore \tan \theta=\frac{2 \sqrt{1^2-0}}{1}$
$\Rightarrow \theta=\tan ^{-1}(2)$

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