A) \[f(x)=\sqrt{{{x}^{2}}-4,}a=2\]
B) \[\sqrt{5}\]
C) \[\sqrt{3}\]
D) \[\sqrt{3}+1\]
Correct Answer: A
Solution :
The equation of a line through P (1,1) and parallel to x + y = 1, is\[\frac{x-1}{\cos \frac{3\pi }{4}}=\frac{y-1}{\sin \frac{3\pi }{4}}\] Let PM = r. Then, the coordinates of M given by \[\frac{x-1}{\cos \frac{3\pi }{4}}=\frac{y-1}{\sin \frac{3\pi }{4}}=r\]is\[\left( 1-\frac{r}{\sqrt{2}},=1+\frac{r}{\sqrt{2}} \right)\] \[\because \]M lies on\[2x-3y-4=0\] \[\therefore \]\[2\left( 1-\frac{r}{\sqrt{2}} \right)-3\left( 1+\frac{r}{\sqrt{2}} \right)-4=0\] \[\Rightarrow \]\[2-\frac{2r}{\sqrt{2}}-3-\frac{3r}{\sqrt{2}}-4=0\]\[\Rightarrow \]\[-5-\frac{5r}{\sqrt{2}}=0\] \[\Rightarrow \]\[r=-\sqrt{2}\] Hence, \[PM=\sqrt{2}\]You need to login to perform this action.
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