If `t_1a n dt_2` are the ends of a focal chord of the parabola `y^2=4a x ,` then prove that the roots of the equation `t_1x^2+a x+t_2=0` are real.

If aa n dc are the lengths of segments of any focal chord of the parabola y^2=2b x ,(b >0), then the roots of the equation a x^2+b x+c=0 are (a)real and distinct (b) real and equal (c)imaginary (d) none of these

If (2,-8) is at an end of a focal chord of the parabola y^2=32 x , then find the other end of the chord.

The focal chord of the parabola y^2=a x is 2x-y-8=0 . Then find the equation of the directrix.

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

The abscissa and ordinates of the endpoints Aa n dB of a focal chord of the parabola y^2=4x are, respectively, the roots of equations x^2-3x+a=0 and y^2+6y+b=0 . Then find the equation of the circle with A B as diameter.

If t_(1) and t_(2) are the extremities of any focal chord of y^(2) = 4ax " then " t_(1)t_(2) is _____

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .

Find the equation of the tangent at t =2 to the parabola y^(2) = 8x .

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2 2geq8.