The length of the portion of the tangent at any point on the curve x^2/3 + y^2/3 = a^2/3 intercepted between the axis is

The equation of the tangent to the curve x² + 2y = 8 which is the perpendicular to x – 2y + 1 = 0 is

For such questions, we should know the formula to find the tangent and slope of lines and curves.

In an isosceles triangle the ends of the base are (2a, 0) and (0, a) and one side is parallel to x – axis. The third vertex is

If x + 2y + 3 = 0, x + 2y – 7 = 0 and 2x – y – 4 = 0 form the sides of square, the equation of the fourth side is

For such questions, we should know properties of square. We should know the formula to find distance between two parallel lines.

The number of real values of k for which the lines x – 2y + 3 = 0, kx + 3y + 1 = 0 and 4x – ky + 2 = 0 are concurrent is

For such questions, we should know properties of concurrent lines.

The distance of the line 2x – 3y = 4 from the point (1, 1) in the direction of the line x + y = 1 is

The mid points of the sides of a triangle are (5, 0), (5, 12) and (0, 12). The orthocentre of this triangle is

The image of the point A (1, 2) by the line mirror y = x is the point B and the image of B by line mirror y = 0 is the point

If

For such questions, we should know different trigonometric formulas. We should simplify the function first before finding derivatives.

If

For such questions, we should know the formulas of inverse functions.

If

For such questions, we should know different formulas.

For such questions, we will use different formulas.

The length of the perpendicular from the incentre of the triangle formed by the axes and the line to the hypotenuse is

If is the angle between two adjacent sides of a parallelogram and p, q are the distances between the parallel sides, then the area of the parallelogram

For such questions, we should know how to use u by v method.

For such questions, we should know u.v method.