Consider a circle `C : x^2+y^2-8y+12=0` and an ellipse `E :(x^2)/(a^2)+(y^2)/(b^2)=1(a > ba n db<2)dot` If the maximum perpendicular distance from the foci of the ellipse upon the tangent drawn to the circle is 7 units, and shortest distance between both the curves is 1 unit, then find the value of `(a^2-2b^2)dot`

Prove that the area bounded by the circle x^2+y^2=a^2 and the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is equal to the area of another ellipse having semi-axis a-b and b ,a > b .

Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/2dot Match the statements in column I with statements in column II Ifa=1a n db=0,t h e n(x , y) , (p) lies on the circle x^2+y^2=1 Ifa=1a n db=1,t h e n(x , y) , (q) l i e son(x^2-1)(y^2-1)=0 Ifa=1a n db=2,t h e n(x , y) , (r) lies on y=x Ifa=2a n db=2,t h e n(x , y) , (s) lies on (4x^2-1)(y^2-1)=0

The locus of the poles of the tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 w.r.t. the circle x^2 + y^2 = a^2 is: (a) parabola (b) ellipse (c) hyperbola (d) circle

The locus of the poles of tangents to the director circle of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 is

Consider the circles C_(1)-=x^(2)+y^(2)-2x-4y-4=0andC_(2)-=x^(2)+y^(2)+2x+4y+4=0 and the line L-=x+2y+2=0 then

The radius of the circle passing through the points of intersection of ellipse x^2/a^2+y^2/b^2=1 and x^2-y^2 = 0 is

The distance of the point (1,-2) from the common chord of the circles x^(2) + y^(2) - 5x +4y - 2= 0 " and " x^(2) +y^(2) - 2x + 8y + 3 = 0

The set of values of 'a' for which the point (a-1, a+1) lies outside the circle x^(2)+y^(2)=8 and inside the circle x^(2)+y^(2)-12x+12y-62=0 , is

Statement 1: The foot of perpendicular from focus on any tangent to ellipse 4x^2 + 5y^2 - 16x + 30y + 41 =0 lie on circle x^2 + y^2 - 4x - 6y + 4 = 0 . Statement 2: The director circle of ellipse x^2/a^2 + y^2/b^2 = 1 is x^2 + y^2 = a^2 + b^2 .

The circle x^(2)+y^(2)-4x-6y-12=0, x^(2)+y^(2)+6x-8y+21=0 are