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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Ellipse

NDA 2016 · Mathematics · Ellipse

If the ellipse 9 x^2+16 y^2=144 intercepts the line 3 x+4 y=12 ,...

If the ellipse 9x2+16y2=1449 x^2+16 y^2=144 intercepts the line 3x+4y=123 x+4 y=12, then what is the length of the chord so formed?

Options

  1. A5 units
  2. B6 units
  3. C8 units
  4. D10 units

Correct answer

A. 5 units

Step-by-step solution

Here, 9 x^2+16 y^2=144 and 3x+4y=12⇒x=12−4y33 x+4 y=12\Rightarrow x=\frac{12-4 y}{3} So, 9(12−4y3)2+16y2=1449\left(\frac{12-4 y}{3}\right)^2+16 y^2=144 On solving we get, y=0,3y=0,3 For y=0;x=4y=0 ; x=4 For y=3;x=0y=3 ; x=0⇒ Length of chord =(0−3)2+(4−0)2=9+16=25=5 units \begin{aligned} \Rightarrow \text{ Length of chord }= & \sqrt{(0-3)^2+(4-0)^2}=\sqrt{9+16} \\ & =\sqrt{25}=5 \text{ units } \end{aligned}$$
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