Conic Sections Question 99
Question: The tangent to the parabola $ y^{2}=4ax $ at the point (a, 2a) makes with x-axis an angle equal to
[SCRA 1996]
Options:
A) $ \frac{\pi }{3} $
B) $ \frac{\pi }{4} $
C) $ \frac{\pi }{2} $
D) $ \frac{\pi }{6} $
Show Answer
Answer:
Correct Answer: B
Solution:
The equation of the tangent at point $ (a,2a) $ of the parabola $ y^{2}=4ax $ is $ yy_1=2a(x+x_1) $
therefore $ 2ay=2a(x+a) $
therefore $ y=x+a $
This line makes an angle of $ \pi /4 $ with the x-axis, as $ m=\tan \theta =1 $ .
BETA
