Mathematics Tes...

If P(at², 2at) be one end of a focal chord of the parabola y² = 4ax, then the length of the chord is

Two tangents are drawn from a point (-2, -1) to the curve y2 = 4x. If α is the angle between them, then |tanα| is equal to

If 2x+3y=α, x−y=β and kx+15y=r are 3 concurrent normals of parabola y2=λx, then the value of k is

If three parabolas touch all the lines x=0, y=0 and x+y=2, then the maximum area of the triangle formed by joining their foci is

An equilateral triangle is inscribed in a parabola y2 = 4ax, where one vertex is

The length of the latus rectum and equation of the directrix of the parabola y²=−8x

The mirror image of the directrix of the parabola y²=4(x+1) in the line mirror x+2y=3, is

The shortest distance (in units) between the parabolas y² = 4x and y²=2x−6 is

(3 + w + 3w²)⁴ equals

The sum of 40 terms of an A.P. whose first term is 2 and common difference 4, will be