Conic Sections (Standard)

Conic Sections: core idea

• 1. Ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$: eccentricity $e=c/a$ with $c=4$: $e$?

  Check

• 2. Hyperbola $\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$: asymptote slope positive?

  Check

• 3. Parabola $y^2=4ax$ with $a=2$: focal length $a$?

  Check

• 4. Circle diameter endpoints $(0,0),(6,0)$: radius?

  Check

• 5. Ellipse major axis length if $a=5$?

  Check

• 6. Line $x=3$ intersects $x^2+y^2=25$: number of points?

  Check

• 7. Focus-directrix parabola $y^2=8x$: $a$?

  Check

• 8. Chord midpoint of $x^2+y^2=r^2$: for midpoint $(1,0)$ on unit circle radius? If chord of $x^2+y^2=4$ midpoint $(1,0)$, half chord length?

  Check

• 9. Normal to $y=x^2$ at $(1,1)$: slope of normal?

  Check