Conic Sections Question 165

Question: Equation of diameter of parabola $ y^{2}=x $ corresponding to the chord $ x-y+1=0 $ is

[RPET 2003]

Options:

A) $ 2y=3 $

B) $ 2y=1 $

C) $ 2y=5 $

D) $ y=1 $

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Answer:

Correct Answer: B

Solution:

Equation of diameter of parabola is $ y=\frac{2a}{m} $

Here $ a=\frac{1}{4},m=1 $

therefore $ y=\frac{2\times 1/4}{1} $
$ \Rightarrow 2y=1 $ .