A line of slope 3 is orthogonal to the circle `x^2+ y^2+ 2x-1=0` and also a tangent to the elipse `x^2/a^2+y^2/b^2=1`, then maximum value of ab is

Let a line L_(1) with slope 1 is a normal to the circle x^(2)+y^(2)+6y+2=0 and tangent to the ellipse " (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , then maximum value of area of ellipse (in square units),is

Let a line L_(1) with slope 1 is a normal to the circle x^(2)+y^(2)+6y+2=0 and tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , then maximum value of area of ellipse (in square units),is

If the line a x+b y=2 is a normal to the circle x^2+y^2-4x-4y=0 and a tangent to the circle x^2+y^2=1 , then

If the line a x+b y=2 is a normal to the circle x^2+y^2-4x-4y=0 and a tangent to the circle x^2+y^2=1 , then a and b are

If the line a x+b y=2 is a normal to the circle x^2+y^2-4x-4y=0 and a tangent to the circle x^2+y^2=1 , then a and b are

If the line a x+b y=2 is a normal to the circle x^2+y^2+4x+4y=0 and a tangent to the circle x^2+y^2=1 , then a and b are

The slope of a common tangent to the ellipse x^(2)//a^(2)+y^(2)//b^(2)=1 and a concentric circle of radius r is

If y=c is a tangent to the circle x^(2)+y^(2)–2x+2y–2 =0 at (1, 1), then the value of c is

Let two parallel lines L_1 and L_2 with positive slope are tangent to the circle C_1 : x^2 + y^2 -2x 16y + 64 = 0 . If L_1 is also tangent to the circle C_2 : x^2 + y^2 - 2x + 2y -2 = 0 and the equation of L_2 is asqrta x - by + c - a sqrta = 0 where a,b,c in N. then find the value of (a+b+c)/7