Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

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) ?

Show that the following curve intersect orthogonally at the indicated point y² = 8x and 2x² +  y² = 10 at  \[\left( 1, 2\sqrt{2} \right)\] ?

Prove that the curves y² = 4x and x² + y² - 6x + 1 = 0 touch each other at the point (1, 2) ?

Find the condition for the following set of curve to intersect orthogonally \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { and } xy = c^2\] ?

Find the condition for the following set of curve to intersect orthogonally \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text { and } \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1\] ?

Show that the curves \[\frac{x^2}{a^2 + \lambda_1} + \frac{y^2}{b^2 + \lambda_1} = 1 \text { and } \frac{x^2}{a^2 + \lambda_2} + \frac{y^2}{b^2 + \lambda_2} = 1\] intersect at right angles ?

If the straight line xcos \[\alpha\] +y sin \[\alpha\] = p touches the curve  \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\] then prove that a²cos^{2 \[\alpha\]} \[-\] b²sin² \[\alpha\] = p² ?