Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Find the equation of the tangent and the normal to the following curve at the indicated points x = θ + sinθ, y = 1 + cosθ at θ = \[\frac{\pi}{2}\] ?

Find the equation of the tangent and the normal to the following curve at the indicated points \[x = \frac{2 a t^2}{1 + t^2}, y = \frac{2 a t^3}{1 + t^2}\text { at } t = \frac{1}{2}\] ?

Find the equation of the tangent and the normal to the following curve at the indicated points x = at², y = 2at at t = 1 ?

Find the equation of the tangent and the normal to the following curve at the indicated points x = a(θ + sinθ), y = a(1 − cosθ) at θ ?

Find the equation of the tangent and the normal to the following curve at the indicated points:

x = 3cosθ − cos3θ, y = 3sinθ − sin3θ? 

Find the equation of the tangent and the normal to the following curve at the indicated points  x = asect, y = btant at t ?

Find the equation of the normal to the curve x² + 2y² − 4x − 6y + 8 = 0 at the point whose abscissa is 2 ?

The equation of the tangent at (2, 3) on the curve y² = ax³ + b is y = 4x − 5. Find the values of a and b ?

Find the equation of the tangent line to the curve y = x² + 4x − 16 which is parallel to the line 3x − y + 1 = 0 ?

Find an equation of normal line to the curve y = x³ + 2x + 6 which is parallel to the line x+ 14y + 4 = 0 ?

Determine the equation(s) of tangent (s) line to the curve y = 4x³ − 3x + 5 which are perpendicular to the line 9y + x + 3 = 0 ?

Find the equation of a normal to the curve y = x log_e x which is parallel to the line 2x − 2y + 3 = 0 ?

Find the equation of the tangent line to the curve y = x² − 2x + 7 which is parallel to the line 2x − y + 9 = 0 ?

Find the equation of the tangent line to the curve y = x² − 2x + 7 which perpendicular to the line 5y − 15x = 13. ?

Find the equations of all lines having slope 2 and that are tangent to the curve \[y = \frac{1}{x - 3}, x \neq 3\] ?

Find the equations of all lines of slope zero and that are tangent to the curve \[y = \frac{1}{x^2 - 2x + 3}\] ?

Find the equation of the tangent to the curve  \[y = \sqrt{3x - 2}\] which is parallel to the 4x − 2y + 5 = 0 ?

Find the equation of the tangent to the curve x² + 3y − 3 = 0, which is parallel to the line y= 4x − 5 ?

Prove that \[\left( \frac{x}{a} \right)^n + \left( \frac{y}{b} \right)^n = 2\] touches the straight line \[\frac{x}{a} + \frac{y}{b} = 2\] for all n ∈ N, at the point (a, b) ?