The equation of a tangent to the parabola, x2 = 8y, which makes an angle $$\theta $$ with the positive directions of x-axis, is :
JEE · Math · previous-year question
- A.x = y cot $$\theta $$ – 2 tan $$\theta $$
- B.y = x tan $$\theta $$ + 2 cot $$\theta $$
- C.x = y cot $$\theta $$ + 2 tan $$\theta $$correct
- D.y = x tan $$\theta $$ – 2 cot $$\theta $$
Answer
C. x = y cot $$\theta $$ + 2 tan $$\theta $$
Explanation
x2 = 8y $$ \Rightarrow $$ $${{dy} \over {dx}} = {x \over 4} = \tan \theta $$ $$ \therefore $$ x1 = 4tan$$\theta $$ y1 = 2 tan2 $$\theta $$ Equation of tangent :- y $$-$$ 2tan2$$\theta $$ = tan$$\theta $$ (x $$-$$ 4tan $$\theta $$) $$ \Rightarrow $$ x = y cot $$\theta $$ + 2 tan $$\theta $$
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