Mathematics Tes...

The equation of a circle C₁ is x² + y² − 4x − 2y − 11 = 0. A circle C₂ of radius 1 unit rolls on the outside of the circle C₁ touching it externally. The locus of the centre of C₂ has the equation

Two vertices of a triangle are (3, -2) and (-2, 3) and its orthocentre is (- 6, 1). The coordinates of its third vertex are-

The equation of the common tangent to the equal parabolas y² = 4ax and x² = 4ay is

A line makes angles of 45° and 60° with the positive directions of x and y axes respectively. An angle, which the line can make with the positive direction of z-axis is:

If ln(x + y) = 2xy, then y′ (0) is equal to

If the fourth term of  is equal to 200 and x > 1, then x is equal to

If the line 3x + 2y = 13 divides the area enclosed by the curve, 9x² + 4y² − 18x − 16y − 11 = 0 into two parts then the ratio of the larger area to the smaller area is

The third vertex of the triangle whose centroid is (7,−2, 5) and whose other two vertices are (2, 6, −4)  and (4,−2, 3)  is

The least positive integral value of m, if