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 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: