Easy Practice — Set 2

Quick Recap — Lines, Circles & Conic Basics

• Angle between lines: $\tan\theta=\left|\dfrac{m_1-m_2}{1+m_1m_2}\right|$; distance of $(x_1,y_1)$ from $ax+by+c=0$: $\dfrac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}$.
• Parabola $y^2=4ax$: focus $(a,0)$, directrix $x=-a$, latus rectum $4a$.
• Ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ ($a>b$): $e=\sqrt{1-\tfrac{b^2}{a^2}}$, foci $(\pm ae,0)$.
• Hyperbola $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$: $e=\sqrt{1+\tfrac{b^2}{a^2}}$, asymptotes $y=\pm\tfrac{b}{a}x$.