List of top Mathematics Questions on Parabola asked in AP EAPCET

The normal drawn to the parabola \[ y^2=8x \] at \((2,4)\) meets the parabola again at the point

If \(a\neq 0\) and the line \[ 2bx+3cy+4d=0 \] passes through the points of intersection of the parabolas \[ y^2=4ax \] and \[ x^2=4ay, \] then

PSQ is a focal chord of the parabola \[ y^2=12x. \] \(A\) and \(B\) are respectively the feet of the perpendiculars drawn from \(P\) and \(Q\) on the directrix of the parabola. If the length of \(AB\) is \(7\sqrt3\) and \[ P=(3t^2,6t), \qquad (0<t<1), \] then \(t=\)

Let \(O\) and \(S\) be the vertex and focus of the parabola \[ y^2=4ax \] respectively and \(x=k\) be its double ordinate of length \(2\sqrt6\,a\). If the line \(x=k\) cuts the \(X\)-axis at \(P\), then the length of the double ordinate drawn through \(O\) to the parabola having \(P\) and \(S\) as vertex and focus is

The product of the slopes of the non-horizontal normals drawn through the point \[ (6,0) \] to the parabola \[ y^2=8x \] is:

If \[ y=mx+\frac{3}{m} \] is a tangent to the parabola \[ y^2=4ax \] at the point \(P(3,\beta)\), where \(\beta<0\), then the value of \[ 3m-\beta \] is:

The equation of the normal to the parabola \[ y^2=12x \] at the point \((3\lambda^2,6\lambda)\) is

The length of the latus rectum of the parabola \[ (x-2)^2+(y-3)^2=\frac{1}{25}(3x-4y+7)^2 \] is

The parabola with focus at \((4,-3)\) and vertex at \((4,-1)\) is

The distance of the point \[ (6,4\sqrt{3}) \] from the focus of \[ y^2=8x \] is:

Which of the following represents a parabola?

Suppose a parabola passes through \((0,4)\), \((1,9)\) and \((4,5)\) and has its axis parallel to the \(y\)-axis. Then the equation of the parabola is