The tangent to the parabola `y^(2)=4(x-1)` at (5,4) meets the line x+y=3 at the point

The normal to the parabola y^(2)=4x at P(9, 6) meets the parabola again at Q. If the tangent at Q meets the directrix at R, then the slope of another tangent drawn from point R to this parabola is

If the tangents to the parabola y^(2)=4ax at (x_1,y_1) and (x_2,y_2) meet on the axis then x_1y_1+x_2y_2=

Two tangents to the parabola y^(2) = 8x meet the tangent at its vertex in the points P & Q. If PQ = 4 units, prove that the locus of the point of the intersection of the two tangents is y^(2) = 8 (x + 2) .

Normal to the parabola y^(2)=8x at the point P(2,4) meets the parabola again at the point Q . If C is the centre of the circle described on PQ as diameter then the coordinates of the image of point C in the line y=x are

The tangent of the circle x^(2)+y^(2)-2x-4y-20=0 at (1,7) meets the y -axis at the point

Find the equation of the tangent to the parabola 3y^(2)=8x, parallel to the line x-3y= 5.

The tangents to the parabola y^(2)=4x at the points (1,2) and (4,4) meet on which of the following lines?

Tangents are drawn from the point (-1,2) to the parabola y^(2)=4x. These tangents meet the line x=2 at P and Q, then length of PQ is

y=2x+3 is a Tangent to the parabola y^(2)=4a(x-(1)/(3)) then 3(a-5)=

If the straight line y=mx+1 be the tangent of the parabola y^(2)=4x at the point (1,2) then the value of m will be-