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, whose coordinate are

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.

Tangents are drawn to x^2+y^2=1 from any arbitrary point P on the line 2x+y-4=0 . The corresponding chord of contact passes through a fixed point whose coordinates are(a) (1/2,1/2) (b) (1/2,1) (c) (1/2,1/4) (d) (1,1/2)

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.

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If 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 through a fixed point (x_2,y_2), then (a) x_1, a ,x_2 in GP (b) (y_1)/2,a ,y_2 are in GP (c) -4,(y_1)/(y_2),x_1/x_2 are in GP (d) x_1x_2+y_1y_2=a^2

If the tangents are drawn from any point on the line x+y=3 to the circle x^2+y^2=9 , then the chord of contact passes through the point. (a) (3, 5) (b) (3, 3) (c) (5, 3) (d) none of these

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 .

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

Consider the relation 4l^(2)-5m^(2)+6l+1=0 , where l,m in R Tangents PA and PB are drawn to the above fixed circle from the points P on the line x+y-1=0 . Then the chord of contact AP passes through the fixed point. (a) ( 1 / 2 , − 5 / 2 ) (b) ( 1 3 , 4 / 3 ) (c) ( − 1 / 2 , 3 / 2 ) (d) none of these

Tangent are drawn from the point (3, 2) to the ellipse x^2+4y^2=9 . Find the equation to their chord of contact and the middle point of this chord of contact.

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.