AP EAMCET · Maths · Parabola
The line \(x-2 y-3=0\) cuts the parabola \(y^2=4 \mathrm{ax}\) at the points P and Q . If the focus of this parabola is \(\left(\frac{1}{4}, k\right)\), then \(P Q=\)
- A \(16 a \sqrt{5}\)
- B \(8 a \sqrt{5}\)
- C \(4 a \sqrt{5}\)
- D \(2 a \sqrt{5}\)
Answer & Solution
Correct Answer
(A) \(16 a \sqrt{5}\)
Step-by-step Solution
Detailed explanation
Given the equation of the parabola \(y^2=4 a x\) and focus of this parabola is \(\left(\frac{1}{4}, k\right)\). \(\Rightarrow(a, 0)=\left(\frac{1}{4}, k\right) \Rightarrow k=0, a=\frac{1}{4}\) Since, \(x-2 y-3=0 \Rightarrow x=2 y+3\) Now,…
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