JEE Main 2019 (Online) 12th April Evening ShiftQuestion 1
An ellipse, with foci at $(0,2)$ and $(0,-2)$ and minor axis of length $4$, passes through which of the following points?
Ellipse
Solution
Formulas used. (1) Ellipse $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ ($a>b$), foci $(0,\pm c)$: $c^2=a^2-b^2$Step 1 - Data. Foci $(0,\pm2)$: $c=2$, major axis along $y$. Minor axis $=2b=4$, so $b=2$. Step 2 - Use (1). $a^2=b^2+c^2=4+4=8$. Ellipse: $\frac{x^2}4+\frac{y^2}8=1$. Step 3 - Test the options. (A) $\frac14+\frac88>1$; (B) $\frac44+\frac28>1$; (D) $\frac44+\frac88=2$. (C) $\frac24+\frac48=\frac12+\frac12=1$ ✓. Answer: C