CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The range of $$\alpha$$, for which the point $$(\alpha, \alpha)$$ lies inside the region bounded by the curves $$y = \sqrt {1 - x^{2}}$$ and $$x + y = 1$$ is


A
12<α<12
loader
B
12<α<13
loader
C
13<α<13
loader
D
14<α<12
loader

Solution

The correct option is B $$\dfrac {1}{2} < \alpha < \dfrac {1}{\sqrt {2}}$$
The point should lies on the opposite side of the origin of the line $$x + y - 1 = 0$$
Then, $$\alpha + \alpha - 1 > 0$$
$$\Rightarrow 2\alpha > 1 \Rightarrow \alpha > \dfrac {1}{2} ..... (i)$$
Also, $$(\alpha^{2} + \alpha^{2}) < 1$$
$$\Rightarrow \left (\dfrac {-1}{\sqrt {2}}\right ) < \alpha < \left (\dfrac {1}{\sqrt {2}}\right ) .... (ii)$$
From Eqs. (i) and (ii), we get
$$\dfrac {1}{2}  < \alpha < \dfrac {1}{\sqrt {2}}$$.
714962_679797_ans_8cecd70083d742efb6c2e38f50d344bf.png

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image