List of top Mathematics Questions on Parabola asked in KEAM

The vertex of the parabola $2y = -3x^2 + 48x - 200$, is
The coordinates of the focus of the parabola given by the equation \(4y - x^2 + 4x - 12 = 0\) are
If the focus and vertex of a parabola are at a distance of 3 units and 6 units, respectively, from the origin on the positive x-axis, then the equation of the parabola is
The axis of a parabola is $x=0$. If the vertex is at a distance 3 from the origin above the x-axis, the vertex of the parabola is at ________.
Find the vertex of the parabola \( 4y = x^2 - 6x + 17 \).
Find the focus of the parabola \( x^2 - 4x + 8y + 4 = 0 \).
If the focus of a parabola is \( (0, -3) \) and its directrix is \( y = 3 \), then its equation is:
The coordinates of the vertex of the parabola \[ y = 2x^2 - 12x + 26 \] are
Find the equation of the parabola with focus at \( (3,1) \) and vertex at \( (5,1) \).
The length of the latus rectum of the parabola \( y^2 = x \) is:
The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an
The area of the region in the first quadrant which is above the parabola \(y = x^2\) and enclosed by the circle \(x^2 +y^2 = 2 \) and the y-axis is
The equation of the parabola with focus (3, 0) and directrix x + 3 = 0 is
The focus of the parabola $y^2 - 4y - x+3=0$ is
The focus of the parabola $( y + 1)^2 = -8(x +2)$ is
The slope of the straight line joining the centre of the circle \( x^2 + y^2 - 8x + 2y = 0 \) and the vertex of the parabola \( y = x^2 - 4x + 10 \) is:
The slope of the straight line joining the centre of the circle \( x^2 + y^2 - 8x + 2y = 0 \) and the vertex of the parabola \( y = x^2 - 4x + 10 \) is:
The slope of the straight line joining the centre of the circle \( x^2 + y^2 - 8x + 2y = 0 \) and the vertex of the parabola \( y = x^2 - 4x + 10 \) is: