List of top Mathematics Questions on sections of a cone asked in MET

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 area of the quadrilateral formed by the tangents at the end point of latus rectum to the ellipse \( \frac{x^2}{9} + \frac{y^2}{5} = 1 \) is
If the line \( y - \sqrt{3}x + 3 = 0 \) cuts the parabola \( y^2 = x + 2 \) at \( A \) and \( B \), then \( PA \cdot PB \) where \( P = (\sqrt{3},0) \) is
$AB$ is a chord of the parabola $y^2 = 4ax$ with vertex $A$. $BC$ is perpendicular to $AB$ meeting axis at $C$. Projection of $BC$ on axis is
The radius of the circle passing through the foci of the ellipse \( \frac{x^2}{4} + \frac{4y^2}{7} = 1 \) and having its centre at \( \left(\frac{1}{2}, 2\right) \) is
The common tangent of the parabolas $y^2 = 4x$ and $x^2 = -8y$ is
\(\log_2(9 - 2^x) = 10^{\log(3-x)}\) solve for \(x\)
In an equilateral triangle, the in-radius, circum-radius and one of the ex-radii are in the ratio
The circles whose equations are \(x^2 + y^2 + c^2 = 2ax\) and \(x^2 + y^2 + c^2 - 2by = 0\) will touch each other externally if
An equilateral triangle \(SAB\) is inscribed in the parabola \(y^2 = 4ax\) having its focus at \(S\). If chord \(AB\) lies towards the left of \(S\), then side length of this triangle is
The circle on focal radii of a parabola as diameter touches
The diameter of \( 16x^2 - 9y^2 = 144 \) which is conjugate to \( x = 2y \) is
The equation of the parabola whose vertex and focus are \( (0, 4) \) and \( (0, 2) \) respectively, is:
The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is 6. The equation of the hyperbola referred to its axes as axes of coordinates are:
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:
The focus of the parabola $y^{2 = 8x}$ is: