List of top Mathematics Questions on Conic sections asked in MHT CET

Find the area of the region bounded by the parabola \( y^2 = 4ax \) and its latus rectum.

The sum of two nonzero numbers is 4. The minimum value of the sum of their reciprocals is

The line passing through the points \( (a, 1, 6) \) and \( (3, 4, b) \) crosses the \( yz \)-plane at \( (0, \frac{17}{2}, -\frac{13}{2}) \), then the value of \( (3a + 4b) \) is

The equation \( x^2 - 3xy + \lambda y^2 + 3x - 5y + 2 = 0 \), where \( \lambda \) is a real number represents a pair of lines. If \( \theta \) is the acute angle between the lines, then \( \frac{\text{cosec}^2 \theta}{\sqrt{10}} = \)}

The equations of the tangents to the circle \( x^2 + y^2 = 36 \) which are perpendicular to the line \( 5x + y - 2 = 0 \) are

The coordinates of the foot of the perpendicular drawn from a point $P(-1, 1, 2)$ to the plane $2x - 3y + z - 11 = 0$ are

The distance between the lines represented by the equation $4x^2 + 4xy + y^2 - 6x - 3y - 4 = 0$ is

The area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 20y$ to the end of its latus rectum is

The area of the region bounded by $\frac{x^2}{9} + \frac{y^2}{4} = 1$ and the line $\frac{x}{3} + \frac{y}{2} = 1$ is

If the curves $y^2 = 6x$ and $9x^2 + by^2 = 16$ intersect each other at right angles, then the value of $b$ is

If $f(x)$ is continuous at point $x = 0$ where $f(x) = \begin{cases} \frac{3\sin x + 5\tan x}{\text{a}^x - 1} & , x<0 \\ \frac{2}{\log 2} & , x = 0 \\ \frac{8x + 2x\cos x}{\text{b}^x - 1} & , x>0 \end{cases}$ then the values of a and b, respectively, are ________

The approximate value of \(\sqrt[3]{64.04}\) is

The coordinates of the foot of the perpendicular drawn from a point $P(-1, 1, 2)$ to the plane $2x - 3y + z - 11 = 0$ are

If the lengths of three vectors $\bar{a}, \bar{b}$ and $\bar{c}$ are 5, 12, 13 units respectively, and each one is perpendicular to the sum of the other two, then $|\bar{a} + \bar{b} + \bar{c}| = ..............$

The foci of a hyperbola coincide with the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$. The equation of the hyperbola with eccentricity 2 is

The function $f(x) = \sin^4 x + \cos^4 x$ increases if}

If the angle between the line $x = \frac{y-1}{2} = \frac{z-3}{\lambda}$ and the plane $x + 2y + 3z = 4$ is $\cos^{-1} \sqrt{\frac{5}{14}}$, then the value of $\lambda$ is