List of top Mathematics Questions on sections of a cone

Let P be a point on the parabola, \( x^2 = 4y \). If the distance of P from the centre of the circle, \( x^2 + y^2 + 6x + 8 = 0 \) is minimum, then the equation of the tangent to the parabola at P, is :
If two tangents from point \((h,k)\) to parabola \(y^2 = 64x\) have slopes such that one is 8 times the other, then value of \( \frac{k^2}{2h} \) is:
The eccentricity of the conic \(9x^2 - 16y^2 = 144\) is
The length of the semi-latus rectum of an ellipse is one third of its major axis, its eccentricity would be
The parabola having its focus at (3,2) and directrix along the y-axis has its vertex at
The locus of the point of intersection of two tangents to the parabola y²=4ax which are at right angle to one another is
Consider the equation of parabola y²+4ax=0 where a>0. Which of the following is correct?
The length of the semi-latus rectum of an ellipse is one third of its major axis. Its eccentricity would be
The parabola having its focus at (3,2) and directrix along the y-axis has its vertex at
The locus of the point of intersection of two tangents to the parabola y²=4ax, which are at right angle to one another is
The eccentricity of an ellipse, with its centre at origin, is \(1/2\). If one of the directrices is \(x=4\), then the equation of the ellipse is
Through the vertex \(O\) of parabola \(y^2=4x\), chords OP and OQ are drawn at right angles to one another. The locus of the midpoint of PQ is
An arch of a bridge is semi-elliptical with major axis horizontal. If the length of the base is \(9\) m and the highest part of the bridge is \(3\) m from the centre of the horizontal axis, the best approximation of the height of the arch \(2\) m from the centre of the base is:
If the line \( 2x - 3y = k \) touches the parabola \( y^2 = 6x \), then find the value of \( k \).
S and T are the foci of an ellipse and B is an end of the minor axis. If \( \triangle \text{STB} \) is an equilateral triangle, then the eccentricity of the ellipse is
An ellipse has OB as semi-minor axis, \( F \) and \( F' \) its foci and the angle \( \angle \text{FBF'} \) is a right angle. Then the eccentricity of the ellipse is
Find the eccentricity of the conic represented by \( x^2 - y^2 - 4x + 4y + 16 = 0 \):
The equation of the ellipse with focus at (±5,0) and eccentricity =(5)/(6) is:
The length of the latus-rectum of the parabola whose focus is ((u²)/(2g)\sin2α,-(u²)/(2g)\cos2α) and directrix is y=(u²)/(2g), is:
The line ax+by=1 cuts ellipse cx²+dy²=1 only once if
If the line 2x-1=0 is the directrix of the parabola y²-kx+6=0, then one of the values of k is
The number of normals drawn to the parabola \( y^{2} = 4x \) from the point \( (1, 0) \) is
The mid point of the chord \( 4x - 3y = 5 \) of the hyperbola \( 2x^{2} - 3y^{2} = 12 \) is
The eccentricity of the conic \( \frac{5}{r} = 2 + 3\cos\theta + 4\sin\theta \) is
The eccentricity of the hyperbola \( x^{2} - 4y^{2} = 1 \) is: