Prove that the curve `x=1-3t^(2), y=t-3t^(3)` is symmetrical with respect to x-axis. If the tangent to the curve makes an angle `psi`with the positive x-axis, show that, `tan psi+-sec psi=3t`.

Find the point on the curve y^2=a x the tangent at which makes an angle of 45^0 with the x-axis.

The point on the curve y^(2)=x , the tangent at which makes an angle 45^(@) with the x- axis is-

Consider the curve x=1-3t^(2),y=t-3t^(2) . If tangent at point (1-3t^(2),t-3t^(2)) inclined at an angle theta to the positive x-axis and another tangent at P(2,-3) cuts the cuve again at Q. The point Q will be-

Consider the curve x=1-3t^(2),y=t-3t^(2) . If tangent at point (1-3t^(2),t-3t^(2)) inclined at an angle theta to the positive x-axis and another tangent at P(2,-3) cuts the cuve again at Q. The value of tan theta+ sec theta is equal to-

Consider the curve x=1-3t^(2),y=t-3t^(2) . If tangent at point (1-3t^(2),t-3t^(2)) inclined at an angle theta to the positive x-axis and another tangent at P(2,-3) cuts the cuve again at Q. The angle between the tangent at P and Q will be-

The slope of the tangent to the curve x= t^(2)+3t-8,y=2t^(2)-2t-5 at the point (2,-1) is

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

If the normal to the curve y=f(x) at the point (3,4) makes an angle (3pi)/4 with the positive x-axis, then f'(3)= (a) -1 (b) -3/4 (c) 4/3 (d) 1

The angle made by the tangent of the curve x = a (t + sint cost) , y = a (1+sint)^(2) with the x-axis at any point on it is

If the tangent t the curv y=f(x )"at" P(x_(1),y_(1)) is paralle to the y-axis, then the of the normal to the curve at P is -