Question

If the double ordinate of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$ passes through the $(5,2),$ then the equation of double ordinate is

• A. $y=2$
• B. $x=5$
• C. $x=6$
• D. $y=4$

Answer 1

The correct option is B $x=5$

Given equation of ellipse is
$\frac{x^2}{36}+\frac{y^2}{16}=1$
It is in the form of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Where $a=6$ and $b=4$
Clearly $a>b$
So, the major axis is along $x-\text{axis},$ while the minor axis is along the $y-\text{axis}.$

Then double ordinate is a chord perpendicular to the major axis.
i.e, $x=\alpha$
As it is passing through the $(5,2)$, so the equation of double ordinate is
$x=5$