List of top Mathematics Questions on Parabola asked in AP EAMCET

If the line \( 5x - 2y - 6 = 0 \) is a tangent to the hyperbola \( 5x^2 - ky^2 = 12 \), then the equation of the normal to this hyperbola at \( (\sqrt{6}, p) \) is:
If \( P \) is a point which divides the line segment joining the focus of the parabola \( y^2 = 12x \) and a point on the parabola in the ratio 1:2, then the locus of \( P \) is:
The normal drawn at a point \( (2, -4) \) on the parabola \( y^2 = 8x \) cuts again the same parabola at \( (\alpha, \beta) \). Then \( \alpha + \beta \) is:
The line \( x - 2y - 3 = 0 \) cuts the parabola \( y^2 = 4ax \) at points P and Q. If the focus of this parabola is \( \left(\frac{1}{4}, k\right) \), then PQ is:
If the angle between the asymptotes of the hyperbola \( x^2 - ky^2 = 3 \) is \( \frac{\pi}{3} \) and e is its eccentricity, then the pole of the line \( x + y - 1 = 0 \) w.r.t. this hyperbola is:
The equation of the normal drawn to the parabola \( y^2 = 6x \) at the point \( (24,12) \) is:
If the ordinates of points \( P \) and \( Q \) on the parabola \[ y^2 = 12x \] are in the ratio 1:2, then the locus of the point of intersection of the normals to the parabola at \( P \) and \( Q \) is:
The locus of the midpoints of the chords of the hyperbola \( x^2 - y^2 = a^2 \) which touch the parabola \( y^2 = 4ax \) is:
If the product of the eccentricities of the ellipse \( \frac{x^2}{16} + \frac{y^2}{b^2} = 1 \) and the hyperbola \( \frac{x^2}{9} - \frac{y^2}{16} = 1 \) is 1, then the value of \( b^2 \) is:
If \(ax+by=1\) is a normal to the parabola
\[ y^2=4px, \] then the condition is
Suppose a parabola with focus at \((0,0)\) has
\[ x-y+1=0 \] as its tangent at the vertex. Then the equation of its directrix is
If a perpendicular drawn through the vertex O of the parabola $y^2=4ax $ to any of its tangent meets the tangent at N and the parabola at M. then ON-OM =