List of top Mathematics Questions on Tangents and Normals

An equation of a common tangent to the parabola $y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} + y^{2} = 4$ is $y = 2x + 2\sqrt{3}$ If the line $y = mx + \frac{4\sqrt{3}}{m}, \left(m\ne0\right)$ is a common tangent to the parabola $y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} + y^{2} = 4$, then m satisfies $m^{4} + 2m^{2} = 24.$

If the normal to the curve $y = f(x)$ at $(3,4)$ makes an angle $\frac{3 \pi}{4}$ with the positive x-axis, then $f'(3)$ is equal to

The normal to the curve $x=a\left(cos\,\theta+\theta\,sin\,\theta \right). y=a\left(sin\,\theta -\theta\,cos\,\theta \right)$ at any point $'\theta'$ is such that :

A function y = f(x) has a second order derivative f''(x) = 6(x - 1).  If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x -5.  then the function is :

The equation of the tangent to the curve $ y={{(1+x)}^{y}}+{{\sin }^{-1}}({{\sin }^{2}}x) $ at $ x=0 $ is:

The chord joining the points $(5, 5)$ and $(11, 227)$ on the curve $y =3x^{2}-11x-15$ is parallel to tangent at a point on the curve. Then the abscissa of the point is

The family of curves whose x and y intercepts of a tangent at any point are respectively double the x and y coordinates of that point is

The subtangent, ordinate and subnormal to the parabola $y^2= 4ax$ at a point (different from the Origin) are in

The angle of intersection to the curve $y = x^2, 6y = 7 - x^3$ at (1, 1) is :

The number of points in $[-2\pi,2\pi]$ , the tangents at which to the curve $y = \sin x$ are perpendicular to the $y-axis$ is

The line $\frac {x} {a} + \frac {y} {b} =1$ touches the curve $y = be^{-x/a}$ at the point

The length of the subtangent to the curve $x^2 + xy + y^2 = 7$ at $ (1, - 3)$ is

Normal at $(1, 1)$ on the curve $2y=9-x^2$ is