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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

Chapter 10

Review

• Conics

• Parabola

• Ellipse

• Circle

• Hyperbola

• Conics

• Rotate (eliminate Bxy)

• Translate (eliminate Dx and Ey) … complete the squares

• Parabola

• Ellipse

• Circle

• Hyperbola

• Parabola

F: (h,k+p)

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

V: (h,k)

dir: y = k–p

• Ellipse

(h,k+b)

V: (h+a,k)

C: (h,k)

F: (h+c,k)

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

• 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

• 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.

C  P

polar axis

P  C

pole

Polar Coordinates

Conversions between Polar and Cartesian

(r, )

r

• 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