A) \[\frac{\sqrt{5}}{6}\]
B) \[\frac{1}{3}\sqrt{\frac{7}{3}}\]
C) \[\frac{1}{6}\sqrt{\frac{7}{3}}\]
D) \[\frac{1}{2}\]
Correct Answer: C
Solution :
\[y={{x}^{3/2}}-2\] \[\frac{dy}{dx}=\frac{3}{2}\sqrt{x}\] |
Slope of normal \[=-\frac{2}{3\sqrt{x}}\] |
Let point is\[({{x}_{1}},x_{1}^{3/2}-2)\] |
\[\therefore \]Normal\[y-(x_{1}^{3/2}-2)=\frac{-2}{3\sqrt{{{x}_{1}}}}(x-{{x}_{1}})\] |
Now put\[(1,7)\]and solve it. \[\Rightarrow \] \[{{x}_{1}}=\frac{1}{3}\] |
\[\therefore \] \[P\Rightarrow \left( \frac{1}{3},7+\frac{1}{3\sqrt{3}} \right),A\Rightarrow (1,7)\] |
\[\therefore \] \[AD=\frac{1}{6}\sqrt{\frac{7}{3}}.\] |
You need to login to perform this action.
You will be redirected in
3 sec