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

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 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 \(x+By+C = 0\) 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 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

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 $a^2 =$