If the tangent at the point `P(2,4)` to the parabola `y^2=8x` meets the parabola `y^2=8x+5` at `Qa n dR ,` then find the midpoint of chord `Q Rdot`

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then find the locus of Pdot

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

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

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

The equation of the directrix of the parabola y^(2)=-8x is

Consider an ellipse (x^2)/4+y^2=alpha(alpha is parameter >0) and a parabola y^2=8x . If a common tangent to the ellipse and the parabola meets the coordinate axes at Aa n dB , respectively, then find the locus of the midpoint of A Bdot

The point of contact of the tangent 2x+3y+9=0 to the parabola y^(2)=8x is:

The line x - y + 2 = 0 touches the parabola y^2 = 8x at the point

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If the tangents at the points Pa n dQ on the parabola y^2=4a x meet at T ,a n dS is its focus, the prove that S P ,S T ,a n dS Q are in GP.