A) \[y=x\,\tan \,\theta +2\,\,\cot \,\theta \]
B) \[y=x\,\tan \,\theta -2\,\cot \theta \]
C) \[x=y\cot \,\theta +2\tan \theta \]
D) \[x=y\,\cot \theta -2\,\tan \theta \]
Correct Answer: C
Solution :
| \[{{x}^{2}}=8y\] |
| \[\Rightarrow \] \[\frac{dy}{dx}=\frac{x}{4}=\tan \theta \] |
| \[\therefore \] \[{{x}_{1}}=4\tan \theta \] |
| \[{{y}_{1}}=2\,\,{{\tan }^{2}}\theta \] |
| Equation of tangent: |
| \[y-2\,\,{{\tan }^{2}}\theta =\tan \,\theta (x-4tan\theta )\] |
| \[x=y\cot \theta +2\,\tan \theta .\] |
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