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

NTA Abhyas 2020 · Mathematics · Parabola

OA is the chord of the parabola y^ 2 = 4x (where O is the origin)....

OAOA is the chord of the parabola y2=4xy^{2} = 4x (where OO is the origin). ABAB is a chord of y2=4xy^{2} = 4x and perpendicular to OAOA which cuts the axis of the parabola at C.C. If the foot of AA on the axis of the parabola is DD, then the length CDCD is equal toOA is the chord of the parabola y^ 2 = 4x (where O is the origin). AB is a chord of y^ 2 = 4x and perpendicular to OA

Options

  1. A22 units
  2. B33 units
  3. C44 units
  4. D66 units

Correct answer

C. 44 units

Step-by-step solution

Let, A = (t2,2t)\left(t^{2}, 2t\right)
OA is the chord of the parabola y^ 2 = 4x (where O is the origin). AB is a chord of y^ 2 = 4x and perpendicular to OA
The slope of OAOA is equal to 2t\dfrac{2}{t}
⇒⇒ The slope of ABAB is equal to −t2- \dfrac{t}{2}
⇒Theequationof⇒The equation ofABis(y−2tx−t2)=−t2is \left(\dfrac{y - 2t}{x - t^{2}}\right) = - \dfrac{t}{2}
⇒C=(4+t2,0)D=(t2,0)<br/>⇒ C = \left(4 + t^{2}, 0\right) D = \left(t^{2}, 0\right)<br />⇒ CD = \left|t^{2} + 4 - t^{2}\right|=4=4& units
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