Find the equation of the straight lines passing through the following pair of point: `(a t_1, a//t_1)` and `(a t_2, a//t_2)`

Find the equation of the straight line passing through the point (2,1) and through the point of intersection of the lines x+2y = 3 and 2x-3y=4

Find the equation of the straight line which passes through the point (1, - 2) and cuts off equal intercepts from axes.

Find the combined equation of the straight lines passing through the point (1,1) and parallel to the lines represented by the equation . x^2-5xy+4y^2+x+2y-2=0 .

Find the equations of the tangent and normal to the parabola y^2=4a x at the point (a t^2,2a t) .

Find the vector equations of the plane passing through the points R(2, 5, -3), S(-2,-3, 5) and T(5, 3, -3).

Find the equations of the tangent to the given curves at the indicated points: x= cos t , y =sin t at t = (pi)/(4)

Write the equation of a tangent to the curve x=t, y=t^2 and z=t^3 at its point M(1, 1, 1): (t=1) .

A particle is moving in a vertical circle with constant speed. The tension in the string when passing through two positions at angles 30^@ and 60^@ from vertical (lowest position) are T_1 and T_2 respectively. Then

Find the equation of tangent to the curve given by x=a sin^(3)t, y=b cos^(3)t at a point where t=(pi)/(2) .