1. Tardigrade
  2. Question
  3. Mathematics
  4. For each point ( x , y ) on the ellipse with centre at the origin and principal axes along the coordinate axes, the sum of the distances from the point (x, y) to the points ( ± 2,0) is 8 . The positive value of x such that ( x , 3) lies on the ellipse, is

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Q. For each point $( x , y )$ on the ellipse with centre at the origin and principal axes along the coordinate axes, the sum of the distances from the point $(x, y)$ to the points $( \pm 2,0)$ is 8 . The positive value of $x$ such that $( x , 3)$ lies on the ellipse, is

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Solution:

image
$ c =2 ; a =4$
equation of the ellipse is
$\left(\frac{x^2}{a^2}+\frac{y^2}{a^2-c^2}=1\right)$
$\frac{x^2}{16}+\frac{y^2}{16-4}=1 \Rightarrow \frac{x^2}{16}+\frac{y^2}{12}=1$
when $y=3$ then $\frac{x^2}{16}+\frac{9}{12}=1 \Rightarrow \frac{x^2}{16}=\frac{1}{4} \Rightarrow x=2$