List of top Mathematics Questions on sections of a cone

If the eccentricity and length of latus rectum of a hyperbola are \(\frac{\sqrt{13}}{3}\) and \(\frac{10}{3}\) units respectively, then what is the length of the transverse axis?

The eccentricity of the ellipse whose major axis is three times the minor axis is:

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 the major axis of an ellipse subtends an angle of $120^{\circ}$ at one end of its minor axis and the length of its semi latus rectum is $\frac{4}{\sqrt{3}}$, then the sum of the lengths of its axes is

The equation of the parabola with focus at $(3, 0)$ and directrix $x + 3 = 0$ is:

The tangents drawn at the points \(P_1\) and \(P_2\) lying on the ellipse \(\frac{x^2}{4}+y^2=1\) are parallel to the chord joining the points \((0,1)\) and \((2,0)\), then the distance between \(P_1\) and \(P_2\) is:

A perpendicular is drawn through the vertex \(O\) of the parabola \(y^2=8x\) to any non-vertical tangent meeting the parabola at \(P\). Then \(OP.OQ=\)

If the eccentricity of a hyperbola is $\sqrt{3}$, then the eccentricity of its conjugate hyperbola is:

If $y=mx+c$, $m>0$ is a common tangent to the parabolas $y^{2}=8x$ and $y^{2}=1+4x$, then $m+c=$

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is:

The line $y = mx + c$ touches the ellipse $9x^2 + 16y^2 = 144$ if the value of $c^2$ is:

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is:

Through the focus of the parabola $x^{2}-4x-8y+44=0$, if tangents are drawn to another parabola $y^{2}=20x$, then the sum of the Y - coordinates of the points of contact of these tangents is

A chord is drawn through the focus of the parabola \(y^2=6x\) such that its perpendicular distance from the vertex is \(\frac{\sqrt5}{2}\). Then its slope can be:

A normal is drawn to the hyperbola \( 9x^{2}-16y^{2}=144 \) at one of the ends of its latus rectum. If that end lies in the third quadrant and the equation of the normal is \( ax+by+c=0 \) then \( \frac{b+c}{a} = \)

The equation of the tangent to the parabola $y^2 = 8x$ which is parallel to the line $2x - y + 5 = 0$ is:

Let S be the focus of the parabola \( y^{2}=36x \) and let the line \( x+by+c=0 \) intersect the parabola at the points Q and R. If the centroid of \( \triangle QRS \) is (57,0), then -c is

The line $y = mx + c$ touches the ellipse $9x^2 + 16y^2 = 144$ if the value of $c^2$ is:

An ellipse intersects the hyperbola \(2x^2-2y^2=1\) orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then the equation of the ellipse is:

If the eccentricity of a hyperbola is $\sqrt{3}$, then the eccentricity of its conjugate hyperbola is:

If the distance of a point P on an ellipse from its focus (1, 2) is half of the distance of P from its corresponding directrix \( x+y=0 \), then the point of intersection of the given directrix and its major axis, is

The equation of the conjugate hyperbola of the hyperbola $x^{2}-4y^{2}-2x-8y-19=0$ is

The equation of the tangent to the parabola $y^2 = 8x$ which is parallel to the line $2x - y + 5 = 0$ is:

If a tangent drawn to the parabola \( y^{2}=16x \) meets the curve \( xy=4 \) at the points P and Q, then the locus of midpoint of PQ is

The equation of the ellipse with foci at \((\pm 3,0)\) and the eccentricity as \(1/3\) is: