Find the angle at which the curve `y=K e^(K x)` intersects the y-axis.

Find the angle at which the parabolas y^2=4x and x^2=32 y intersect.

Tangent is drawn at the point (x_i ,y_i) on the curve y=f(x), which intersects the x-axis at (x_(i+1),0) . Now, again a tangent is drawn at (x_(i+1,)y_(i+1)) on the curve which intersect the x-axis at (x_(i+2,)0) and the process is repeated n times, i.e. i=1,2,3dot,ndot If x_1,x_2,x_3,ddot,x_n from an arithmetic progression with common difference equal to (log)_2e and curve passes through (0,2)dot Now if curve passes through the point (-2, k), then the value of k is____

Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin and makes an angle of 30^0 with the positive direction of the x-axis.

Let y=e^(x^2) and y=e^(x^2) sinx be two given curves. Then the angle between the tangents to the curves any point of their intersectons is

Find the angle between the curves 2y^2=x^3 and y^2=32 x .

Find the equation of the tangent and normal to each of the following curves at the specified points : y(x-2)(x-3)+7=x and the point, the where curve intersect the x-axis.

The circle with equation x^2 +y^2 = 1 intersects the line y= 7x+5 at two distinct points A and B. Let C be the point at which the positive x-axis intersects the circle. The angle ACB is

Let y=e^(x^(2))" and "y=e^(x^(2))sinx be two given curves. Then the angle between the tangents to the curves at any point of their intersection is-

Let y=e^(x^(2)) and y=e^(x^(2))sinx be two given curves. Then the angle between the tangents to the curves at any point of their intersection is

Find the area bounded by the curve y=x(x-1)^(2) , the y-axis and the line y=2.