List of top Mathematics Questions on Conic sections asked in MET

The points on the curve \(xy^2 = 1\) which are nearest to the origin, are

The area bounded by the parabolas \(y^2 = 4a(x + a)\) and \(y^2 = -4a(x - a)\) is

The foci of the conic section \(25x^2 + 16y^2 - 150x - 175 = 0\) are

All the chords of the hyperbola \(3x^2 - 2y^2 - 4x + y = 0\), subtending a right angle at the origin pass through the fixed point

If \(f(x) = \frac{\sin(e^x - 2) - 1}{\log(x - 1)}\), then \(\lim_{x \to 2} f(x)\) is given by

The greatest value of the function \(f(x) = xe^{-x}\) in \([0, \infty)\), is

The eccentricity of the conic \(x^2 - 4x + 4y^2 = 12\) is

Two common tangents to the circle \(x^2 + y^2 = 2a^2\) and parabola \(y^2 = 8ax\) are

The value of the integral $\int_π/2³π/2[sin~x]dx$, where $[·]$ denotes the greatest integer function, is

If the equation $lx²+2mxy+ny²=0$ represents a pair of conjugate diameters of the hyperbola $x²/a² - y²/b² = 1$, then

If $e$ is the eccentricity of the hyperbola $x²/a² - y²/b² = 1$ and $θ$ is the angle between the asymptotes, then $\cos(θ/2)$ is equal to

The equation $3x²+7xy+2y²+5x+5y+2=0$ represents

To the lines $ax²+2hxy+by²=0$ the lines $a²x²+2h(a+b)xy+b²y²=0,$ are