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TS EAMCET · Maths · Parabola

The length of the latusrectum of the conic \(25\left[(x-2)^2+(y-3)^2\right]=(3 x-4 y+7)^2\) is

  1. A \(\frac{1}{5}\)
  2. B \(\frac{2}{5}\)
  3. C \(\frac{3}{5}\)
  4. D \(\frac{4}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2}{5}\)

Step-by-step Solution

Detailed explanation

Given, 25[(x-2) \(\left.)^2+(y-3)^2\right]=[3 x-4 y+7]^2\) is \[ \Rightarrow(x-2)^2+(y-3)^2=\left(\frac{3 x-4 y+7}{\sqrt{25}}\right)^2 \] Its focus \(\equiv(2,3)\), Directrix \(\rightarrow 3 x-4 y+7\) \(\therefore L=\) length of latus rectum \(=2\) (distance between focus and…