Conic Sections Question 319
Question: The length of the chord of the parabola $ y^{2}=4ax $ which passes through the vertex and makes an angle $ \theta $ with the axis of the parabola, is
Options:
A) $ 4a\cos \theta cose{c^{2}}\theta $
B) $ 4a{{\cos }^{2}}\theta cosec\theta $
C) $ a\cos \theta cose{c^{2}}\theta $
D) $ a{{\cos }^{2}}\theta cosec\theta $
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=x\tan \theta $ will be equation of chord. The points of intersection of chord and parabola are (0, 0), $ ( \frac{4a}{{{\tan }^{2}}\theta },\ \frac{4a}{\tan \theta } ) $
Hence length of chord $ =4a\sqrt{{{( \frac{1}{{{\tan }^{2}}\theta } )}^{2}}+\frac{1}{{{\tan }^{2}}\theta }} $
$ =\frac{4a}{\tan \theta }\sqrt{\frac{1+{{\tan }^{2}}\theta }{{{\tan }^{2}}\theta }}=4a\text{ cose}{c^{2}}\theta \cos \theta $ .
BETA
