Question

Daje naj.!

Zad.1

Znajdz wspolrzedne punktow wspolnych prostej i okregu:

a)x-2y-2=0

xkwadrat+(y-1)kwadrat=24/5

b)y=-2x+3

(x+3)kwadrat+ ykwadrat=4

c)3x-y+1=0

(x-3)kwadrat+ ykwadrat=10

Answer 1

 a)x-2y-2=0
xkwadrat+(y-1)kwadrat=24/5

 

x=2y+2

x²+(y-1)²=24/5

x=2y+2

(2y+2)²+y²-2y+1=24/5

 

4y²+8y+4+y²-2y+1=24/5

5y²+6y+5=24/5

5y²+6y+5-24/5=0

5y²+6y+1/5=0

Δ=36-4*5*1/5=36-20*1/5=36-4=32

√Δ=4√2

y1=(-6-4√2)/10=-3/5-2√2/5

y2=(-6+4√2)/10=-3/5+2√2/5 

 

x1=2y1+2=2*(-3/5-2√2/5)+2=-6/5-4√2/5+2=4/5-4√2/5

x2=2y2+2=2*(-3/5+2√2/5)+2=-6/5+4√2/5+2=4/5+4√2/5 

 

b)y=-2x+3
(x+3)kwadrat+ ykwadrat=4

y=-2x+3

(x+3)²+y²=4

 

y=-2x+3

x²+6x+9+(-2x+3)²=4

x²+6x+9+4x²-12x+9-4=0

5x²-6x+14=0

Δ=36-4*5*14=36-20*14=36-280=-244

brak punktow wspolnych 

c)3x-y+1=0
(x-3)kwadrat+ ykwadrat=10

 

-y=-3x-1

(x-3)²+y²=10

 

y=3x+1

x²-6x+9+y²=10

 

y=3x+1

x²-6x+9+(3x+1)²-10=0

x²-6x+9+9x²+6x+1-10=0

10x²=0

x²=0

x=0

 

y=3x+1=3*0+1=1

 

jeden punkt wspolny:

x=0

y=1

 

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