MCA Entrance Previous Year Question Bank

The locus of the mid-point of all chords of the parabola $y^2=4x$, which are drawn through its vertex is:

Focus of the parabola $x^2+y^2-2xy-4(x+y-1)=0$ is:

The vertex of parabola $y^2-8y-x+19=0$ is:

If the tangents at the extremities of a focal chord of the parabola $x^2=4ay$ meet the tangent at the vertex at points whose abscissa are $x_1$ and $x_2$, then $x_1{x}_2=$

If $x=1$ is the directrix of the parabola $y^2=kx-8$, then $k$ is:

An equilateral triangle is inscribed in the parabola $y^2=4ax$, such that one of the vertices of the triangle coincides with the vertex of the parabola. The length of the side of the triangle is:

The vertex of the parabola whose focus is $(-1,1)$ and directrix is $4x+3y-24=0$ is

Find the area bounded by the line $y=3-x,$ the parabola y = x² - 9 and x ≥ -4, y ≥ 0.

The coordinates of the focus of the parabola $4y^2+12x-20y+67=0$ are

A point P in the first quadrant, lies on $y^2=4ax$, a>0, and keep a distance of $5a$ unit from its focus. Which of the following points lies on the locus of P?