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

NTA Abhyas 2020 · Mathematics · Parabola

The length of the chord of the parabola x^ 2 = 4y having equation x...

The length of the chord of the parabola x2=4yx^{2} = 4y having equation x−2y+42=0x - \sqrt{2}y + 4\sqrt{2} = 0 isThe length of the chord of the parabola x^ 2 = 4y having equation x - 2 y + 4 2 = 0 is

Options

  1. A636\sqrt{3} units
  2. B828\sqrt{2} units
  3. C2112\sqrt{11} units
  4. D323\sqrt{2} units

Correct answer

A. 636\sqrt{3} units

Step-by-step solution

Solving the equations of the given parabola and the line, we get,

(2y−42)2=4y⇒y2−10y+16=0⇒∣y1−y2∣=(y1+y2)2−4y1y2=100−64=6\left(\sqrt{2}y - 4\sqrt{2}\right)2 = 4y ⇒ y^{2} - 10y + 16 = 0 ⇒ \left|{y}_{1} - {y}_{2}\right| = \sqrt{\left({y}_{1} + {y}_{2}\right)2 - 4{y}_{1}{y}_{2}} = \sqrt{100 - 64} = 6

The length of the chord of the parabola x^ 2 = 4y having equation x - 2 y + 4 2 = 0 is

⇒⇒ Length of the chord =AB=(x1−x2)2+(y1−y2)2=2(y1−y2)2+(y1−y2)2=3∣y1−y2∣= AB = \sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}} = \sqrt{2{\left({y}_{1} - {y}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}} = \sqrt{3}\left|{y}_{1} - {y}_{2}\right|

=63= 6\sqrt{3}
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