PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Find the points on the curve y = x³ where the slope of the tangent is equal to the x-coordinate of the point ?

Find the equation of the tangent to the curve \[\sqrt{x} + \sqrt{y} = a\] at the point \[\left( \frac{a^2}{4}, \frac{a^2}{4} \right)\] ?

Find the equation of the normal to y = 2x³ − x² + 3 at (1, 4) ?

Find the equation of the tangent and the normal to the following curve at the indicated point y = x⁴ − bx³ + 13x² − 10x + 5 at (0, 5)  ?

 Find the equation of the tangent and the normal to the following curve at the indicated point y = x⁴ − 6x³ + 13x² − 10x + 5 at x = 1? 

Find the equation of the tangent and the normal to the following curve at the indicated point  y = x² at (0, 0) ?

Find the equation of the tangent and the normal to the following curve at the indicated point y = 2x² − 3x − 1 at (1, −2) ?

Find the equation of the tangent and the normal to the following curve at the indicated point \[y^2 = \frac{x^3}{4 - x}at \left( 2, - 2 \right)\] ?

Find the equation of the tangent and the normal to the following curve at the indicated point y = x² + 4x + 1 at x = 3  ?

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

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

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) ?