Tangent of a Curve y =f(x)

Q. If m is slope of common tangents y = $x^2$ - x + 1, y = $x^2$ - 3x + 1 then m is

1. None of these
2. 7
3. 9
4. 16

Q.

If the slope of the curve $y=\frac{ax}{b-x}$ at the point (1, 1) is 2 then values of a and b respectively

1. 1, 2

2. -1, 2

3. None of these

4. 1, -2

Q.

If the line y = 2x touches the curve y = ax^2 + bx + c at the point where x = 1 and the curve passes through the point (-1, 0), then the values of a, b, c are

1. 
   

2. 
   

3. 
   

4. None of these

Q. For the curve y = 3sin $\theta cos\theta ,x=e^{\theta }sin\theta ,0\le \theta \le \pi$; tangent is parallel to x-axis, then $\theta$ =

1. 0
2. 
3. 
4. 

Q.

Number of possible tangents to the curve $y=cos(x+y),-3\pi \le x\le 3\pi$ that are parallel to the line x+2y = 0, is

1. 2

2. 3

3. 4

4. 1

Q.

The slope of the tangent to the curve $x=t^2+3t-8,y=2t^2-2t-5$ at the point t = 2 is

1. 6/7

2. 5/6

3. 1

4. 7/6

Q.

The angle between the tangents to the curve $y^2=2ax$ at the points where $x=\frac{a}{2}$, is

1. π/6

2. π/3

3. π/4

4. π/2

Q.

Tangents are drawn from the origin to the curve y = sin x. Their points of contact lie on the curve

1. x²y²=y+x

2. x²y²=x²-y²

3. None of these

4. x²y²=x²+y²

Q.

The chord joining the points where x =p and x=q on the curve $y=a{x}^2+bx+c$ is parallel to the tangent at the point on the curve whose abscissa is

1. 
   

2. 
   

3. 
   

4. None of these

Q.

Tangents are drawn from the origin to the curve y = sin x, then their point of contact lie on the curve

1. 
   

2. 
   

3. 
   

4.