Let S be the set of points, whose abscissae and ordinates are natural numbers. Let p e S, such that the sum of the distance of P from (8, 0) and (0, 12) is minimum among all elemants in S. Then, the number of such points P in S is
1
3
5
11
If in a ABC, AD, BE and CF are the altitudes and R is the circumradius, then the radius of the circumcircle of DEF is
None of these
The line through the points (a, b) and (- a,- b) passes through the point
(1, 1)
(3a, - 2b)
(a2, ab)
(a, b)
The equation x3 - yx2 + x - y = 0 represents
a hyperbola and two straight lines
a straight line
a parabola and two straight lines
a straight line and a circle
The coordinates of a point on the line x + y + 1 = 0, which is at a distance unit from the line 3x + 4y + 2 = 0, are
(2, - 3)
(- 3, 2)
(0, - 1)
(- 1, 0)
Number of points having distance from the straight line x - 2y + 1 = 0 and a distance is from the line 2x + 3y - 1 = 0, is
1
2
4
5
The straight lines x + y = 0, 5x + y = 4 and x + 5y = 4 form
an isosceles triangle
an equilateral triangle
a scalene triangle
a right angled triangle
If z = x + iy, where x and y are real numbers and i = , then the points (x, y) for which is real, lie on
an ellipse
a circle
a parabola
a straight line
The equation 2x2 + 5xy - 12y2 = 0 represents a
circle
pair of non-perpendicular intersecting straight lines
pair of perpendicular straight lines
hyperbola
The number oflines which pass through the point (2, - 3) and are at a distance 8 from the point (- 1, 2) is
infinite
4
2
0