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 every point on the line x+y=4 ,tangents are drawn to circle x^(2)+y^(2)=4 .Then,all chord of contact passes through (x_(1),y_(1)),x_(1)+y_(1)=

Tangents are drawn from the points on the line x-y-5=0 to x^(2)+4y^(2)=4. Then all the chords of contact pass through a fixed point. Find the coordinates.

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 point on line y=x+k ,tangents are drawn to (x^(2))/(2)-(y^(2))/(1)=1 such that chords of contact pass through a fixed point (a,b) then (a)/(b)=

If from a variable point 'P' on the line 2x-y-1=0 pair of tangent's are drawn to the parabola x^(2)=8y then prove that chord of contact passes through a fixed point,also find that 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 circle x^2+y^2=a^2 tangents are drawn to the hyperbola x^2-y^2=a^2 . Then, the locus of mid-points of the chord of contact of tangents is: