From a variable point p on line `2x−y-1=0` pair of tangents are drawn to parabola `x^2=8y` then chord of contact passes through a fixed point.

From a point on the line x-y+2=0 tangents are drawn to the hyperbola (x^(2))/(6)-(y^(2))/(2)=1 such that the chord of contact passes through a fixed point (lambda, mu) . Then, mu-lambda is equal to

From points on the straight line 3x-4y + 12 = 0, tangents are drawn to the circle x^2 +y^2 = 4 . Then, the chords of contact pass through a fixed point. The slope of the chord of the circle having this fixed point as its mid-point is

From a point on the line y=x+c , c(parameter), tangents are drawn to the hyperbola (x^(2))/(2)-(y^(2))/(1)=1 such that chords of contact pass through a fixed point (x_1, y_1) . Then , (x_1)/(y_1) is equal to

Tangents are drawn from the points on a tangent of the hyperbola x^2-y^2=a^2 to the parabola y^2=4a xdot If all the chords of contact pass through a fixed point Q , prove that the locus of the point Q for different tangents on the hyperbola is an ellipse.

From any point on the line (t+2)(x+y) =1, t ne -2 , tangents are drawn to the ellipse 4x^(2)+16y^(2) = 1 . It is given that chord of contact passes through a fixed point. Then the number of integral values of 't' for which the fixed point always lies inside the ellipse is

From a variable point R on the line y = 2x + 3 tangents are drawn to the parabola y^(2)=4ax touch it at P and Q point. Find the locus of the centroid of the triangle PQR.

Tangents are drawn to x^(2)+y^(2)=1 from any arbitrary point P on the line 2x+y-4=0 .Prove that corresponding chords of contact pass through a fixed point and find that point.

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

Tangent is drawn at any point (x_1,y_1) on the parabola y^2=4ax . Now tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass throught a fixed point (x_2,y_2) Prove that 4(x_1/x_2)+(y_1/y_2)^2=0 .

Show that the line x- y +4=0 is tangent to the parabola y^(2)= 16x . Find the point of contact.