ExamBro
ExamBro
AP EAMCET · Maths · Ellipse

\(A B\) is a line segment moving between the axes such that ' \(A\) ' lies on \(X\)-axis and ' \(B\) ' lies on \(Y\)-axis. If \(P\) is a point on \(A B\) such that \(P A=b\) and \(P B=a\), then the equation of locus of \(P\) is

  1. A \(\frac{x^2}{b^2}+\frac{y^2}{a^2}=1\)
  2. B \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
  3. C \(\frac{x^2}{2 a^2}+\frac{y^2}{2 b^2}=1\)
  4. D \(\frac{x^2}{2 b^2}+\frac{y^2}{a^2}=1\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Step-by-step Solution

Detailed explanation

\[ \text { Let } P(h, k) \text { be any point in the locus } \mathrm{cm} \] Let \(A=(x, 0), B=(0, y)\) Given, \(P A=b, P B=a\) In \(\triangle P M A\), \[ \sin \theta=\frac{k}{b} \] In \(\triangle B N P\), \[ \cos \theta=\frac{h}{a} \] We have,…