Exam Exam

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 d) None of them

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) d) None of them

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 d) None of them

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 d) None of them