The line joining two points A(2, 0), B(3, 1) is rotated about A in anti-clockwise direction through an angle of 15°. The equation of the line in the now position, is
√3x - y - 2√3 = 0
x - 3√y - 2 = 0
√3x + y - 2√3 = 0
x - √3y - 2 = 0
The number of integral points (integral points means both the coordinates should be integer) exactly in the interior of the triangle with vertices (0, 0), (0, 21) and (21, 0) is
133
190
233
105
If a tangent having slope of - to the ellipse intersects the major and minor axes in points A and B respectively, then the area of is equal to (O is centre of the ellipse)
12 sq units
48 sq units
64 sq units
24 sq units
D.
24 sq units
Let P(x1, y1) be a point on the ellipse.
The equation of the tangent at (x1, y1) is . This meets the axes at . It is given that slope of the tangent at (x1, y1) is
If PQ is a double ordinate of hyperbola (x2/a2) - (y2/b2) = 1 such that OPQ is a equilateral triangle, O being the centre of the hyperbola, then the eccentricity 'e' of the hyperbola satisfies
1 < e < 2/√3
e = 2/√3
e = √3/2
e > 2/√3
The sides AB, BC and CA of a have respectively 3, 4 and 5 points lying on them. number of triangles that can be constructed using these points as vertices is
205
220
210
None of these
P is a fixed point (a, a, a) on a line through the origin is equally inclined to the axes, then any plane through P perpendicular to Op, makes intercepts on the axes, the sum of whose reciprocal is equal to
a
None of these