Geometria analitica Flashcards by Aurora Pasquetto

Q

Punti verticali

A

y2 - y1 |

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Q

Punti orizzontali

A

x2 - x1 |

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Q

Punti in generale

A

/( x2 - x1 )^2 + ( y2 - y1 )^2

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Q

Retta equazione lineare

A

ax + by + c = 0

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Q

Retta equazione canonica

A

y = mx + q

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Q

Punto con retta passante

A

y - y0 = m( x - x0 )

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Q

Punti con retta

A

x - x1 \ x2 - x1 = y - y1 \ y2 - y1

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Q

Retta con punti su asse x e y

A

x \ p + y \ q = 1

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Q

Punto medio

A

( x1 + x2 \ 2 ; y1 + y2 \ 2 )

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Q

Distanza punto retta

A

d = | ax0 + by0 + c | \ /a^2 + b^2

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Q

Conica equazione generale

A

F ( x , y ) = Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

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Q

Circonferenza equazione normale

A

x^2 + y^2 + ax + by + c = 0

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Q

Circonferenza equazione generale

A

kx^2 + ky^2 + kax + kby + kc = 0

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Q

Centro coordinate (circonferenza)

A

( xC = -a \ 2 ; yC = -b \ 2 )

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Q

Raggio (circonferenza)

A

r = / xC^2 + yC^2 + c

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Q

Ellisse definizione

A

PF1 + PF2 = 2a

Q

Ellissi equazione canonica (con punto medio nell’origine e fuochi sull’asse x)

A

x^2 \ a^2 + y^2 \ b^2 = 1

Q

Relazione 3 parametri (ellisse)

A

c^2 = a^2 - b^2

Q

Eccentricità (ellisse)

A

e = c \ a

e compresa tra 0 e 1

Q

Parabola equazione normale

A

y = ax^2 + bx + c

Q

Fuoco (parabola)

A

F = (-b \ 2a ; -A+1 \ 4a)

Q

Direttrice (parabola)

A

y = -A-1 \ 4a

Q

Asse di simmetria (parabola)

A

x = -b \ 2a

Q

Vertice (parabola)

A

V = ( -b \ 2a ; -A / 4a )

Parabola asse y

x = ay^2 + by + c Cambio y con x nelle formule

Iperbole definizione

| PF1 + PF2 | = 2a

Iperbole equazione canonica

x^2 \ a^2 + y^2 \ b^2 = 1

Relazione 3 parametri (iperbole)

c^2 = a^2 + b^2

Eccentricità (iperbole)

e = c \ a

Asintoti (iperbole)

``` y = -bx \ a y = bx \ a ```

Iperbole equilatera equazione

xy = k