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

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 ?

Find the angle of intersection of the following curve \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and x² + y² = ab ?

Find the angle of intersection of the following curve  x² + 4y² = 8 and x² − 2y² = 2 ?

Find the angle of intersection of the following curve  x² = 27y and y² = 8x ?

Find the angle of intersection of the following curve x² + y² = 2x and y² = x ?

Find the angle of intersection of the following curve y = 4 − x² and y = x² ?

Show that the following set of curve intersect orthogonally y = x³ and 6y = 7 − x² ?

Show that the following set of curve intersect orthogonally x³ − 3xy² = −2 and 3x²y − y³ = 2 ?

Show that the following set of curve intersect orthogonally x² + 4y² = 8 and x² − 2y² = 4 ?

Show that the following curve intersect orthogonally at the indicated point x² = 4y and 4y + x² = 8 at (2, 1) ?

Show that the following curve intersect orthogonally at the indicated point x² = y and x³ + 6y = 7 at (1, 1) ?