Analyzing Polar Equations for Conic Sections

Key Questions

• How do I find the directrix and focus of a parabola?

  There are two basic kinds of parabola(as it is convenient for me to say)

  Type 1:
  The parabola lying on, or parallel to the `x-`axis

  This parabola is of the form `(y-y_v)^2=4a(x-x_v)`

  Where,
  - focus is `(a+x_v,y_v)`
  - directrix is the line `x=x_v-a`
  - Vertex is `(x_v,y_v)`

  Type 2:
  The parabola lying on, or parallel to the `y-`axis

  This parabola is of the form `(x-x_v)^2=4a(y-y_v)`

  Where,
  - focus is `(x_v,a+y_v)`
  - directrix is the line `y=y_v-a`
  - Vertex is `(x_v,y_v)`

  Antoine · 1 · Apr 18 2015
• How do I find the directrix of a hyperbola?

  Answer:

  The directrix is the vertical line `x=(a^2)/c`.

  Explanation:

  For a hyperbola `(x-h)^2/a^2-(y-k)^2/b^2=1`,

  where `a^2+b^2=c^2`,

  the directrix is the line `x=a^2/c`.

  

  mason m · 14 · Jan 1 2016

• How do I find the directrix and focus of a parabola?
• How do I find the directrix of a hyperbola?
• How do I find the directrix of the parabola whose equation is `y=x^2/32`?
• How do I find the directrix of the parabola `y=2x^2`?
• Where is the vertical directrix of a conic if the denominator of its polar equation has the form `1-e cosq`?
• How do you find the points of intersection of the curves with polar equations `r=6costheta` and `r=2+2costheta`?
• How do you find the eccentricity, directrix, focus and classify the conic section `r=0.8/(1-0.8sintheta)`?
• How do you find the eccentricity, directrix, focus and classify the conic section `r=2/(1+2costheta)`?
• How do you find the eccentricity, directrix, focus and classify the conic section `r=10/(2-2sintheta)`?
• How do you find the eccentricity, directrix, focus and classify the conic section `r=8/(4-1.6sintheta)`?
• How do you find the eccentricity, directrix, focus and classify the conic section `r=14.4/(2-4.8costheta)`?
• How do you name the curve given by the conic `r=6`?
• How do you name the curve given by the conic `r=4/(1+costheta)`?
• How do you name the curve given by the conic `r=4/(1+2sintheta)`?
• How do you name the curve given by the conic `theta=(2pi)/3`?
• How do you name the curve given by the conic `r=6/(2+sintheta)`?