Let A (-2, 0) and B(2, 0), then the number of integral values of a, `a in [-10, 10] for which line segment AB subtends an acute angle at point C (a, a+1) is

Find the number of integral values of 'a' for which ax^2 - (3a + 2)x + 2(a + 1) < 0, a != 0 holds exactly four integral value of x.

If A(0, 0), B(1, 0) and C(1/2,sqrt(3)/2) then the centre of the circle for which the lines AB,BC, CA are tangents is

P and Q are two points on a line passing through (2, 4) and having slope m. If a line segment AB subtends a right angles at P and Q, where A(0, 0) and B(6,0), then range of values of m is

Find the locus of a point at which the angle subtended by the line segment joining (1, 2) and (-1, 3) is a right angle.

The co-ordinates of A, B, C are respectively (-4, 0), (0, 2) and (-3, 2). Find the co-ordinates of the point of intersection of the line which bisects the angle CAB internally and the line joining C to the middle point of AB is

A straight line passes through the point of Intersection of the lines x- 2y - 2 = 0 and 2x - by - 6= 0 and the origin, then the set of values of 'b' for which the acute angle between this line and y=0 is less than 45^@ is

Find the locus of a point such that the line segments having end points (2,0) and (-2,0) subtend a right angle at that point.

Let A(a,0) and B(b,0) be fixed distinct points on the x-axis, none of which coincides with the O(0,0) , and let C be a point on the y-axis. Let L be a line through the O(0,0) and perpendicular to the line AC. The locus of the point of intersection of the lines L and BC if C varies along is (provided c^2 +ab != 0 )

Let 2a+2b+c=0 , then the equation of the straight line ax + by + c = 0 which is farthest the point (1,1) is

A variable straight line of slope 4 intersects the hyperbola xy=1 at two points. Then the locus of the point which divides the line segment between these two points in the ratio 1:2 , is (A) x^2 + 16y^2 + 10xy+2=0 (B) x^2 + 16y^2 + 2xy-10=0 (C) x^2 + 16y^2 - 8xy + 19 = 0 (D) 16x^2 + y^2 + 10xy-2=0