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`

If a tangent to the parabola y^(2)=4ax intersects the (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at A and B, then the locus of the point of intersection of tangents at A and B to the ellipse is

if a variable tangent of the circle x^(2)+y^(2)=1 intersects the ellipse x^(2)+2y^(2)=4 at P and Q. then the locus of the points of intersection of the tangents at P and Q is

The chords passing through (2, 1) intersect the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 at A and B. The locus of the point of intersection of tangents at A and B on the hyperbola is

If normal of circle x^(2)+y^(2)+6x+8y+9=0 intersect the parabola y^(2)=4x at P and Q then find the locus of point of intersection of tangent's at P and Q.

Two tangents are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that product of their slope is c^(2) the locus of the point of intersection is

If PQ is the focal chord of the parabola y^(2)=-x and P is (-4, 2) , then the ordinate of the point of intersection of the tangents at P and Q is

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at Aa n dB . The locus of the point of intersection of tangents at Aa n dB to the circle x^2+y^2=9 is x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 y^2-x^2=((27)/7)^2 (d) none of these

If the tangent drawn to the hyperbola 4y^2=x^2+1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid-point of AB is:

Statement-1: The tangents at the extrenities of a forcal of the parabola y^(2)=4ax intersect on the line x + a = 0. Statement-2: The locus of the point of intersection of perpendicular tangents to the parabola is its directrix