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MTH 253 – Calculus. Chapter 10 Review. Conics and Quadratic Equations. Conics Parabola Ellipse Circle Hyperbola. Conics and Quadratic Equations. Conics Rotate (eliminate Bxy ) Translate (eliminate Dx and Ey ) … complete the squares Parabola Ellipse Circle Hyperbola.

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mth 253 calculus

MTH 253 – Calculus

Chapter 10

Review

conics and quadratic equations
Conics and Quadratic Equations
  • Conics
      • Parabola
      • Ellipse
      • Circle
      • Hyperbola
conics and quadratic equations1
Conics and Quadratic Equations
  • Conics
      • Rotate (eliminate Bxy)
      • Translate (eliminate Dx and Ey) … complete the squares
      • Parabola
      • Ellipse
      • Circle
      • Hyperbola
conics and quadratic equations2
Conics and Quadratic Equations
  • Parabola

F: (h,k+p)

P: (h+2p,k+p)

V: (h,k)

dir: y = k–p

conics and quadratic equations3
Conics and Quadratic Equations
  • Ellipse

(h,k+b)

V: (h+a,k)

C: (h,k)

F: (h+c,k)

dir: x = h+a2/c = h+a/e

conics and quadratic equations4
Conics and Quadratic Equations
  • Hyperbola

asy: y = (b/a)(x-h)+k

(h,k+b)

V: (h+a,k)

C: (h,k)

F: (h+c,k)

dir: x = h+a2/c = h+a/e

conics and quadratic equations5
Conics and Quadratic Equations
  • Polar Forms

Eccentricity

Parabola: e = 1

Ellipse: 0 < e < 1

Hyperbola: e > 1

dir: x = k

F: (0,0)

V: (ek/(1+e),0)

F: (0,0)

Other Orientations:

Directrix below.

Directrix above.

Directrix left.

polar coordinates

C  P

polar axis

P  C

pole

Polar Coordinates

Conversions between Polar and Cartesian

(r, )

r

graphs of polar equations
Graphs of Polar Equations
  • Graph common polar curves
    • circles, limaçons, flowers/roses, lemniscate
    • inequalities
    • slopes (formula will be given)
    • Intersections
      • solve as system of equations
      • check graph
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