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Ispravak pisane provjere znanja - krivulje

Total questions: 15

Worksheet time: 12mins

Name
Class
Date
1.

Jednadžba krivulje na slici glasi

a)

x2 5+y2 3=1\frac{x^{2\ }}{5}+\frac{y^{2\ }}{3}=1

b)

x2 25−y2 9=1\frac{x^{2\ \ }}{25}-\frac{y^{2\ }}{9}=1

c)

x2 25+y2 9=1\frac{x^{2\ \ }}{25}+\frac{y^{2\ }}{9}=1

d)

x2 5+y2 3=1\frac{x^{2\ }}{5}+\frac{y^{2\ }}{3}=1

2.

Jednadžba krivulje na slici glasi 

a)

 x2  4−y2 2=1\frac{x^{2\ \ }}{4}-\frac{y^{2\ }}{2}=1  

b)

 x2  2−y2 1=1\frac{x^{2\ \ }}{2}-\frac{y^{2\ }}{1}=1  

c)

 x2  4+y2 1=1\frac{x^{2\ \ }}{4}+\frac{y^{2\ }}{1}=1  

d)

 x2  4+y2 2=1\frac{x^{2\ \ }}{4}+\frac{y^{2\ }}{2}=1  

3.

Jednadžba krivulje na slici glasi

a)

x2 =6yx^{2\ }=6y

b)

x2 =−6yx^{2\ }=-6y

c)

y2 =−6xy^{2\ }=-6x

d)

y2 =6xy^{2\ }=6x

4.

Odredi veliku i malu poluos zadane elipse x249+y216=1\frac{x^2}{49}+\frac{y^2}{16}=1 

(a)  

5.

Parabola zadana jednadžbom ima otvor prema

a)

desno

b)

gore

c)

lijevo

d)

dolje

6.

odredi linearni ekscentricitet hiperbole

a)

34\sqrt{34}

b)

3434

c)

1616

d)

44

7.

Fokus zadane parabole se nalazi u kojoj točki?

a)

F(−34, 0)F\left(-\frac{3}{4},\ 0\right)

b)

F(34,0)F\left(\frac{3}{4},0\right)

c)

F(−32, 0)F\left(-\frac{3}{2},\ 0\right)

d)

F(32, 0)F\left(\frac{3}{2},\ 0\right)

8.

Odredi jednadžbu elipse sa slike

a)
b)
c)
d)
9.

Odredi fokuse elipse zadane formulom 3x2+8y2=1203x^2+8y^2=120  

a)

 F(±4,0)F\left(\pm4,0\right)  

b)

 F(±5,0)F\left(\pm5,0\right)  

c)

 F(0,±5)F\left(0,\pm5\right)  

d)

 F(0,±4)F\left(0,\pm4\right)  

10.

točka T(6,5) nalazi se na elipsi čija je velika poluos 9. Odredi jednadžbu elipse.

a)

x29+y25=1\frac{x^2}{9}+\frac{y^2}{5}=1

b)

x281+y225=1\frac{x^2}{81}+\frac{y^2}{25}=1

c)

x29+y245=1\frac{x^2}{9}+\frac{y^2}{45}=1

d)

x281+y245=1\frac{x^2}{81}+\frac{y^2}{45}=1

11.

Paraboli  y2=4xy^2=4x   koordinate fokusa su

a)

 F(2,0)F\left(2,0\right)  

b)

 F(1,0)F\left(1,0\right)  

c)

 F(−2,0)F\left(-2,0\right)  

d)

 F(−1,0)F\left(-1,0\right)  

12.

Paraboli  x2=2yx^2=2y  jednadžba ravnalice je

a)

 x=12x=\frac{1}{2}  

b)

 x=−12x=-\frac{1}{2}  

c)

 y=−12y=-\frac{1}{2}  

d)

 y=12y=\frac{1}{2}  

13.

Pravac x+2y−7=0x+2y-7=0 siječe elipsu x2+4y2=25x^2+4y^2=25 u:

(a)  

14.

Odredi jednadžbu tangente elipse 3x228+4y27=1\frac{3x^2}{28}+\frac{4y^2}{7}=1  u točki  D(−1,x>0)D\left(-1,x>0\right)  . Jednadžbu zapiši u implicitnom obliku.

(a)  

15.

 Odredi realnu i imaginarnu poluos te linearni ekscentricitet dane krivulje 64x2−225y2=12960064x^2-225y^2=129600 

(a)