AP EAMCET · Maths · Parabola
The length of the latusrectum of the parabola \((x-2)^2+(y-3)^2=\frac{1}{25}(3 x-4 y+7)^2\) is
- A \(\frac{1}{5}\)
- B \(\frac{2}{5}\)
- C \(\frac{3}{5}\)
- D \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{2}{5}\)
Step-by-step Solution
Detailed explanation
Given, equation of parabola is \[ \begin{aligned} & (x-2)^2+(y-3)^2=\frac{1}{25}(3 x-4 y+7)^2 \\ & \Rightarrow 25\left[(x-2)^2+(y-3)^2\right]=(3 x-4 y+7)^2 \end{aligned} \] Focus of the parabola \(=(2,3)\) Equation of directrix \(=3 x-4 y+7\) Length of latus rectum is twice the…
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