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) 287x2 - 28y2 + 423x - 72y -108xy + 144 = 0
b) 287x2 + 28y2 + 423x - 72y -108xy + 144 = 0
c) 287x2 - 28y2 + 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 4x2 + 4y2 -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) x2 + y2 - 6y - 16 = 0
b) x2 + y2 - 6x - 25 = 0
c) x2 + y2 - 6x - 16 = 0
d) x2 + y2 - 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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