JEE Mains · Maths · STD 12 - 6. Application of derivatives
The equation of a tangent to the parabola, \(x^2 = 8y,\) which makes an angle \(\theta \) with the positive direction of \(x-\) axis, is
- 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 \(x = y\,\cot \,\theta \, - 2\,\tan \,\theta \)
Answer & Solution
Correct Answer
(C) \(x = y\,\cot \,\theta \, + 2\,\tan \,\theta \)
Step-by-step Solution
Detailed explanation
\({x^2} = 8y\) \( \Rightarrow \frac{{dy}}{{dx}} = \frac{x}{4} = \tan \theta \) \(\therefore {x_1} = 4\tan \theta \) \({y_1} = 2{\tan ^2}\theta \) Equation of tangent :- \(y - 2{\tan ^2}\theta = \tan \theta \left( {x - 4\tan \theta } \right)\)…
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