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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Parabola

NTA Abhyas 2020 · Mathematics · Parabola

The locus of the middle points of the chords of the parabola y^ 2 =...

The locus of the middle points of the chords of the parabola y2=4ax,y^{2} = 4ax, which passes through the origin is

Options

  1. Ay2=axy^{2} = ax
  2. By2=2axy^{2} = 2ax
  3. Cy2=4axy^{2} = 4ax
  4. Dx2=4ayx^{2} = 4ay

Correct answer

B. y2=2axy^{2} = 2ax

Step-by-step solution

Let mid point be(x1,y1)( {x}_{1}, {y}_{1} )

∴∴ Equation of chord is

T=S1T = {S}_{1}

yy1−2a(x+x1)=y12−4ax1{yy}_{1} - 2a\left(x + {x}_{1}\right) = {y}_{1}^{2} - 4a{x}_{1}

Since, it passes through origin

∴−2ax1=y12−4ax1∴ - 2a{x}_{1} = {y}_{1}^{2} - 4a{x}_{1}

⇒y12=2ax1⇒ {y}_{1}^{2} = 2a{x}_{1}

∴∴ Locus isy2=2axy^{2} = 2ax
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