A) \[4a\cos \theta \,\text{cose}{{\text{c}}^{2}}\,\theta \]
B) \[4a{{\cos }^{2}}\theta \,\text{cosec}\,\theta \]
C) \[a\cos \theta \,\text{cose}{{\text{c}}^{2}}\,\theta \]
D) \[a{{\cos }^{2}}\theta \,\text{cosec}\,\theta \]
Correct Answer: A
Solution :
\[y=x\tan \theta \] will be equation of chord. The points of intersection of chord and parabola are (0, 0), \[\left( \frac{4a}{{{\tan }^{2}}\theta },\ \frac{4a}{\tan \theta } \right)\] Hence length of chord \[=4a\sqrt{{{\left( \frac{1}{{{\tan }^{2}}\theta } \right)}^{2}}+\frac{1}{{{\tan }^{2}}\theta }}\] \[=\frac{4a}{\tan \theta }\sqrt{\frac{1+{{\tan }^{2}}\theta }{{{\tan }^{2}}\theta }}=4a\text{ cose}{{\text{c}}^{2}}\theta \cos \theta \].
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