List of top Mathematics Questions on Tangents and Normals asked in MHT CET

The equation of the normal to the curve \[ y=\log_e x \] at the point $P(1,0)$ is:

The equation of normal to the curve \[ y=\log_e x \] at the point \(P(1,0)\) is

For the curve \( y = 3x^3 - 3x^2 + 1 \) at \( x = 1 \), find the equation of the tangent.

The length of the perpendicular drawn from the origin on the normal to the curve $x^2 + 2xy - 3y^2 = 0$ at the point $(2, 2)$ is ______.

The equation of the tangent to the curve $(1 + x^2)y = 2 - x$, where it crosses the X-axis, is ______.

The equation of the tangent to $y=be^{-x/a}$ at the point where it crosses the Y axis is}

The area of the triangle formed by the co-ordinate axes and a tangent to the curve $xy = a^2$ at the point $(x_1, y_1)$ is ______ sq. units (where $a, x_1$ and $y_1$ are non-zero)

The area of the triangle formed by the co-ordinate axes and a tangent to the curve $xy = a^2$ at the point $(x_1, y_1)$ is ______ sq. units (where $a, x_1$ and $y_1$ are non-zero)

The area of the triangle formed by the co-ordinate axes and a tangent to the curve $xy = a^2$ at the point $(x_1, y_1)$ is ______ sq. units (where $a, x_1$ and $y_1$ are non-zero)

If $y = 4x - 5$ is a tangent to the curve $y^{2} = px^{3} + q$ at $(2, 3)$, then $p-q$ is

The point on the curve $y^2 = 2(x - 3)$ at which the normal is parallel to the line $y - 2x + 1 = 0$ is

The equation of the tangent to the curve $y = \sqrt{2} \sin\left(2x + \frac{\pi}{4}\right)$ at $x = \frac{\pi}{4}$ is

The curves $\frac{x^2}{a^2} + \frac{y^2}{4} = 1$ and $y^3 = 16x$ intersect each other orthogonally, then $a^2 =$

The abscissa of the points, where the tangent to the curve $y = x^3 - 3x^2 - 9x + 5$ is parallel to $X$ axis are

The equation of the tangent to the curve $y = 4x e^x$ at $\left(-1, -\frac{4}{e}\right)$ is

Let the curve be represented by $x=2(\cos t+t\sin t)$, $y=2(\sin t-t\cos t)$. Then normal at any point '$t$' of the curve is at a distance of _____ units from the origin.