Mathematics Tes...

The vertex of the parabola x²=8y−1 is:

Directions: The following question has four choices, out of which ONE or MORE can be correct.

Let h(x) = f(x) - (f(x))² + (f(x))³ for every real number x. Then,

If t₁ and t₂ are the ends of a focal chord of the parabola y²=2x then:

Directions: The following question has four choices, out of which ONE or MORE can be correct.

Three lines px + qy + r = 0, qx + ry + p = 0 and rx + py + q = 0 are concurrent, if:

Let PQ be a chord of the parabola y² = 4x. A circle drawn with PQ as diameter passes through the vertex V of the parabola. If area of ΔPVQ = 20 square units then coordinates of P are:

A double ordinate of the parabola y²=8px is of length 16p. The angle subtended by it at the vertex of the parabola is

The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x=0 and y=0 is:

The equation of the directrix of the parabola y²+4y+4x+2=0 is:

The parabola y²−2x−6y+5=0 has :

Directions: The following question has four choices, out of which ONE or MORE can be correct.

The equation(s) of the tangents drawn from the origin to the circle x² + y² + 2rx + 2hy + h² = 0 is/are:

Tangent is drawn at any point P of a curve which passes through (1, 1) cutting x-axis and y-axis at A and B, respectively. If BP : AP = 3 : 1, then

The nature of the intercepts made on the axes by the tangent at the point (16/5,9/5) to the ellipse 9x²+16y²=144 are:

The distance of a point P on the ellipse x²+3y²=6 from the centre is 2 the eccentric angle of P is:

Find the latus rectum of the parabola x²+2y−3x+5=0 ?

Equation of the two tangents drawn from (2,−1) to x²+3y²=3 are: