List of top Mathematics Questions on Tangents and Normals

At any point on the curve \[ by^2=(x+a)^3, \] if the length of the sub-tangent (ST) and the length of the sub-normal (SN) are such that \[ p(\text{SN})=q(\text{ST})^2, \] then \[ \frac{p}{q}= \]

If the tangent drawn at \((\sqrt2,1)\) on the circle \[ x^2+y^2=3 \] is also a tangent to the two circles of equal radius \(2\sqrt3\) with centres at \[ (0,\beta_1) \quad \text{and} \quad (0,\beta_2), \] then \[ |\beta_1-\beta_2|= \]

If P and Q are the points of intersection of the straight line $x=1$ and the curve $x^{2}+xy+y^{2}=7$ then the acute angle between the normals drawn at P and Q is}

The slope of the normal to the curve $y = 2x^2 + 3\sin x$ at $x = 0$ is:

The line \(x+y = 0\) touches the curve \(y^2 = ax^3+b\) at \((1,-1)\) then values of \(a\) and \(b\) respectively are ...........

If the line \(ax+by+5 = 0\) is a normal to the curve \(xy = 1\) then .....

If the line \(x+By+C = 0\) is the normal to the curve given by \(x = asin^3t\), \(y = bcos^3t\), (where \(a,b\neq 0\)) at a point \(t = \frac{π}{2}\), then \(B-C =\)

If the tangent to the curve \(xy+ax+by = 0\) at \((1,1)\) makes an angle of \(tan^{-1}2\) with positive direction of the \(x\)-axis, then the value of \(\frac{ab}{a+b}\) is...

If the line \(y = 4x-5\) is tangent to the curve \(y^2 = ax^3+b\) at the point \((2,3)\), then the value of \(7a-2b\) is...

The equation of tangent to the curves \(x = 1-3t^2\) and \(y = t-3t^3\) at the point \((-2,2)\) is...

The point on the curve \(9y^2 = x^3\) where the normal to the curve makes equal intercepts with the co-ordinate axes is

The co-ordinates of the point on the curve \(y = xlogx\) at which the normal is parallel to the line \(2x-2y = 3\) are...

If the tangent to the curve \(2y^3 = x^3+ax^2\) at the point \((a,a)\) cuts off intercepts \(α\) and \(β\) on the coordinate axes such that \(α^2+β^2 = 61\), then the value of \(a\) is

The equation of the normal to the curve \(xy+7 = 0\) is \(Ax+By+C = 0\), then

The tangent to the curve \(y^2-xy+9 = 0\) is vertical when

The equation of the tangent to the curve \(y = 3x^3-3x^2+x\) at \(x = 1\) is

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

If the equation of the tangent to the parabola $y^2=4ax$ at the point $(at^2,2at)$ is perpendicular to the line $x+y=1$, then the value of $t$ is:

Let \(P\) be any point on the curve \(x^{2/3}+y^{2/3}=a^{2/3}\). Then, what would be the length of the segment of the tangent between the coordinate axes?

If \(x + 13y = 40\) is normal to the curve \(y = 5x^{2} + \alpha x + \beta\) at the point (1,3), then the value of \(\alpha\beta\) is equal to:

Find the equation of the normal to a parabola which is perpendicular to a given line. This involves:

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}