AP EAMCET · Maths · Parabola
The point \((3,4)\) is the focus and \(2 x-3 y+5=0\) is the directrix of a parabola. Its latusrectum is
- A \(\frac{2}{\sqrt{13}}\)
- B \(\frac{4}{\sqrt{13}}\)
- C \(\frac{1}{\sqrt{13}}\)
- D \(\frac{3}{\sqrt{13}}\)
Answer & Solution
Correct Answer
(A) \(\frac{2}{\sqrt{13}}\)
Step-by-step Solution
Detailed explanation
Given that focus of parabola is \((3,4)\) and equation of directrix is \(2 x-3 y+5=0\) As we know, Length of the latusrectum \(=2 \times\) Length of perpendicular from focus on directrix \(=\left|\frac{2 \times 3-3 \times 4+5}{\sqrt{2^2+(-3)^2}}\right|=\frac{2}{\sqrt{13}}\)
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