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` .

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

If (x+1, y-2)=(3,1), find the values of x and y.

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x_1,y_1) and (x_2,y_2), respectively, then x_1=y^2 (b) x_1=y_1 y_1=y_2 (d) x_2=y_1

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

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.

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.

Find the length of the common chord of the parabola y^2=4(x+3) and the circle x^2+y^2+4x=0 .

If log ((x+y)/3)=1/2 (log x +log y) then find the value of x/y+y/x

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

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.