A) \[\frac{ab}{b-a}\]
B) \[\frac{b}{b-a}\]
C) \[\frac{a}{b-a}\]
D) \[\frac{ba}{a-b}\]
Correct Answer: A
Solution :
Length of latusrectum of the parabola \[{{y}^{2}}=4ax\]is\[4a\]. \[\because \] Intercept points are b and k. \[\therefore \]latusrectum, \[4a=4.\frac{bk}{b+k}\] \[\Rightarrow \] \[a=\frac{bk}{b+k}\] \[\Rightarrow \] \[ab+ak=bk\] \[\Rightarrow \] \[k(b-a)=ab\] \[\Rightarrow \] \[k=\frac{ab}{b-a}\]
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