1.- The equation of the locus of the points in the plane whose distance to the origin is three times the distance to the staight line 6x - y + 4 = 0 is

a) 287x^{2} - 28y^{2} + 423x - 72y -108xy + 144 = 0

b) 287x^{2} + 28y^{2} + 423x - 72y -108xy + 144 = 0

c) 287x^{2} - 28y^{2} + 423x - 72y + 144 = 0

d) None of them

2.- The equation of the perpendicular bisector of the segment AB, where A(1,-1) and B(-3,4), is

a) 8x + 10y + 23 = 0

b) 8x - 10y - 23 = 0

c) 8x - 10y + 23 = 0

3.- The coordinates of the centroid of the triangle that the points (3,4), (2,-1) and (4,0) form are

a) (1,3)

b) (3,1)

c) (3,-1)

d) (-1,3)

4.- The coordinates of the circumcentre of the triangle that the points (2,3), (6,9) and (8,1) form are

a) (65,52)

b) (65/11,52/11)

c) (-1/11,52/11)

5.- The coordinates of the orthocentre of the triangle that the points (2,3), (6,9) and (8,1) form are

a) (65/11,52/11)

b) (-65/11,52/11)

c) (46/11,39/11)

d) (46,39)

6.- The coordinates of the centre and the radius of the circumference 4x^{2} + 4y^{2} -10x + 5y - 1 = 0 are

a) C(5/4,-5/8); r = √141/8

b) C(-5/4,5/8); r = √141/8

c) C(5/4,-5/8); r = 141/64

7.- Find the equation of the circumference whose centre is (-3,0) and its radius is 5

a) x^{2} + y^{2} - 6y - 16 = 0

b) x^{2} + y^{2} - 6x - 25 = 0

c) x^{2} + y^{2} - 6x - 16 = 0

d) x^{2} + y^{2} - 25 = 0

8.- Calculate the eccentricity of the ellipse

a) e = 0.5

b) √3/2

c) -√3/2

d) 0.9

9.- Calculate the eccentricity of the hyperbola

a) e = √5/9

b) e = 4

c) e = 3

d) e = √5/2

10.- If the vertex of a parabola is the point (1,0), then the parameter p equals

a) 1/2

b) 2

c) 0

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