Mathematics Tes...

The locus of a variable point whose distance from the point (2, 0) is 2/3 times its distance from the line x = 9/2 is

The locus of a point such that two tangents drawn from it to the parabola y² = 4ax are such that the slope of one is double the other is

T is a point on the tangent to a parabola y² = 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then

Tangents are drawn from the points on the line x – y + 3 = 0 to parabola y² = 8x. Then the variable chords of contact pass through a fixed point whose coordinates are

The focus of the parabola x²−8x+2y+7 = 0 is

From the focus of the parabola y² = 8x as centre, a circle is described so that a common chord of the curves is equidistant from the vertex and focus of the parabola. The equation of the circle is

In an examination, ten students scored the following marks: 60, 58, 90, 51, 47, 81, 70, 95, 87, 99. The range of this data is

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