Mth 253 calculus
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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


Polar areas

Polar: Areas