List of top Mathematics Questions on Tangents and Normals asked in AP EAPCET

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

The normal to the curve \[ x=a(1+\cos\theta), \quad y=a\sin\theta \] at \(\theta\) always passes through a fixed point, then the fixed point is

If \(m\) is the slope of a tangent to the curve \(e^y=1+x^2\) at \(x=1\), then \(m=\)

\(V\) is the set of points on the curve \(y^3-3xy+2=0\) where the tangent is vertical, then \(V=\)

The equation of tangent of the curve \[ y=\sqrt{9-2x^2} \] at the point where the ordinate and abscissa are equal is

If the line \[ ax+by+c=0 \] is a normal to the curve \[ xy=1, \] then:

The area of the triangle formed by the tangent to the curve \[ xy=a^2 \] at \((x_1,y_1)\) on it and the axes is

If the slope of the line through \((0,0)\) which is tangent to the curve \[ y=x^2+x+16 \] is \(m\), then the value of \[ m-4 \] is:

If the normal drawn at a point \(P\) on the curve \[ 3y=6x-5x^3 \] passes through \((0,0)\), then the positive integral value of the abscissa of the point \(P\) is

The line joining the points \((0,3)\) and \((5,-2)\) is a tangent to the curve \[ y=\frac{C}{x+1} \] then \(C=\)

The number of those tangents to the curve \[ y^2-2x^3-4y+8=0 \] which pass through the point \((1,2)\) is

If the straight line \[ x\cos\alpha+y\sin\alpha=p \] touches the curve \[ \left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\right)^n=2 \] at the point \((a,b)\) on it and \[ \frac{1}{a^2}+\frac{1}{b^2}=\frac{k}{p^2}, \] then \(k=\)

If the angle between the curves \(y^2=4x\) and \(y=e^{-x/2}\) is \(\theta\), then \(\cosec^2\left(\dfrac{\theta}{2}\right)\) is

The least intercept made by a tangent to the ellipse \(\dfrac{x^2}{64}+\dfrac{y^2}{49}=1\) with coordinate axes is

The angle made by the tangent at \(\theta=\dfrac{\pi}{3}\) on the curve \(x=a(\theta+\sin\theta)\), \(y=a(1-\cos\theta)\) with \(x\)-axis is