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AP EAMCET201922 Apr 2019Morning ShiftMathematicsStraight LinesActual

A straight line meets the (X ) and (Y ) axes at the points (A, B ) respectively. If (A B=6 ) units, then the locus of the point (P ) which divides the line segment (A B ) such that (A P: P B=2: 1 ), is

Options

  1. A(3 x^2+y^2=36 )
  2. B(4 x^2+y^2=36 )
  3. C(3 x^2+y^2=16 )
  4. D(4 x^2+y^2=16 )

Correct answer

D. (4 x^2+y^2=16 )

Step-by-step solution

Let (A(a, 0) ) and (B(0, b) ) and point (P(h, k) ) divides the line (A B ). Now, ( aligned & P(h, k)= ( a 1+0 1+2 , 0 2 b 1+2 ) & P(h, k)= ( a 3 , 2 b 3 ) & h= a 3 and k= 2 b 3 & b= 3 k 2 aligned ) ( a=3 h ) and Also, given that (A B=6 ) ( aligned & (a-0)^2+(0-b)^2 =6 & a^2+b^2=36 & 9 h^2+ 9 k^2 4 =36 & h^2+ k^2 4 =4 & 4 h^2+k^2=16 aligned ) ( ) Required locus of (P ) is (4 x^2+y^2=16 ).

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