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AP EAMCET · Maths · Circle

If the locus of the mid points of the chords of the circle \(x^2+y^2=25\), which subtend a right angle at the origin is given by \(\frac{x^2}{a^2}+\frac{y^2}{a^2}=1\) then \(|a|=\)

  1. A \(\frac{2}{5}\)
  2. B \(\frac{5}{\sqrt{2}}\)
  3. C \(\frac{2}{25}\)
  4. D \(5 \sqrt{2}\)
Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

\(x^2+y^2=25 \Rightarrow r=5\) Let midpoint of chord \(A B\) be \(C\) \(\sin \frac{\pi}{4}=\frac{\mathrm{BC}}{\mathrm{OB}} \Rightarrow \mathrm{BC}=\frac{5}{\sqrt{2}}\) Let co-ordinates of C be \(\left(x_1, y_1\right)\) By Pythagoras theorem…