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

Find the equation of the tangent and the normal to the following curve at the indicated point  \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( a\sec\theta, b\tan\theta \right)\] ?

Find the equation of the tangent and the normal to the following curve at the indicated point y² = 4ax at \[\left( \frac{a}{m^2}, \frac{2a}{m} \right)\] ?

Find the equation of the tangent and the normal to the following curve at the indicated point \[c^2 \left( x^2 + y^2 \right) = x^2 y^2 \text { at }\left( \frac{c}{\cos\theta}, \frac{c}{\sin\theta} \right)\] ?

Find the equation of the tangent and the normal to the following curve at the indicated point xy = c² at \[\left( ct, \frac{c}{t} \right)\] ?

Find the equation of the tangent and the normal to the following curve at the indicated point \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text { at } \left( x_1 , y_1 \right)\] ?

Find the equation of the tangent and the normal to the following curve at the indicated point \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( x_0 , y_0 \right)\] ?

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

 Find the equation of the tangent and the normal to the following curve at the indicated point  x² = 4y at (2, 1) ?

Find the equation of the tangent and the normal to the following curve at the indicated point  y² = 4x at (1, 2)  ?

Find the equation of the tangent and the normal to the following curve at the indicated point 4x² + 9y² = 36 at (3cosθ, 2sinθ) ?    

Find the equation of the tangent and the normal to the following curve at the indicated point  y² = 4ax at (x₁, y₁)?

Find the equation of the tangent and the normal to the following curve at the indicated point \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( \sqrt{2}a, b \right)\] ?

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 ?