Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

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) ?

Find the equation of the tangent to the curve x = sin 3t, y = cos 2t at

\[t = \frac{\pi}{4}\] ?

At what points will be tangents to the curve y = 2x³ − 15x² + 36x − 21 be parallel to x-axis ? Also, find the equations of the tangents to the curve at these points ?

Find the equation of  the tangents to the curve 3x² – y² = 8, which passes through the point (4/3, 0) ?

Find the angle of intersection of the following curve y² = x and x² = y  ?

Find the angle of intersection of the following curve  y = x² and x² + y² = 20  ?

Find the angle of intersection of the following curve  2y² = x³ and y² = 32x ?

Find the angle of intersection of the following curve x² + y² − 4x − 1 = 0 and x² + y² − 2y − 9 = 0 ?