From a point, perpendicular tangents are drawn to the ellipse `x^ + 2y^2 =2`. The chord of contact touches a circle concentric with the given ellipse. The ratio of the maximum and minimum areas of the circle is…

From a point P perpendicular tangents PQ and PR are drawn to ellipse x^(2)+4y^(2) =4 , then locus of circumcentre of triangle PQR is

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.

Number of perpendicular tangents that can be drawn on the ellipse (x^(2))/(16)+(y^(2))/(25)=1 from point (6, 7) is

Let from a point A (h,k) chord of contacts are drawn to the ellipse x^2+2y^2=6 such that all these chords touch the ellipse x^2+4y^2=4, then locus of the point A is

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

Statement 1 : If there is exactly one point on the line 3x+4y+5sqrt(5)=0 from which perpendicular tangents can be drawn to the ellipse (x^2)/(a^2)+y^2=1,(a >1), then the eccentricity of the ellipse is 1/3dot Statement 2 : For the condition given in statement 1, the given line must touch the circle x^2+y^2=a^2+1.

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

Tangents drawn from (2, 0) to the circle x^2 + y^2 = 1 touch the circle at A and B Then.

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.

Find the equations of the tangent drawn to the ellipse (x^(2))/(3) + y^(2) =1 from the point (2, -1 )