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AP EAMCET · Maths · Parabola

The length of the latus rectum of the parabola \(169\left\{(x-1)^2+(y-3)^2\right\}=(5 x-12 y+17)^2\) is

  1. A \(\frac{14}{13}\)
  2. B \(\frac{12}{13}\)
  3. C \(\frac{28}{13}\)
  4. D \(\frac{56}{13}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{28}{13}\)

Step-by-step Solution

Detailed explanation

Given parabola, \(\begin{array}{cc} & 169\left[(x-1)^2+(y-3)^2\right]=(5 x-12 y+17)^2 \\ \Rightarrow & (x-1)^2+(y-3)^2=\left(\frac{5 x-12 y+17}{13}\right)^2 \\ \Rightarrow & (S P=P M) \end{array}\) Here, focus is \(S(1,3)\) and directrix \((5 x-12 y+17)=0\) \(\therefore\)…