Medium Practice — Set 2

Quick Recap — Conics (JEE Application)

• Ellipse $\tfrac{x^2}{a^2}+\tfrac{y^2}{b^2}=1$: $e^2=1-\tfrac{b^2}{a^2}$, foci $(\pm ae,0)$, LR $=\tfrac{2b^2}{a}$, sum of focal distances $=2a$; tangent $y=mx\pm\sqrt{a^2m^2+b^2}$.
• Parabola $y^2=4ax$: point $(at^2,2at)$, focal distance $x+a$, tangent $ty=x+at^2$, tangent condition $c=\tfrac am$.
• Hyperbola $\tfrac{x^2}{a^2}-\tfrac{y^2}{b^2}=1$: $e^2=1+\tfrac{b^2}{a^2}$, tangent $y=mx\pm\sqrt{a^2m^2-b^2}$, asymptotes $y=\pm\tfrac ba x$.