The line `x+y=k` will cut the circle `x^2 + y^2 - 4x - 6y + 5 = 0` at two distinct points if (A) `klt1` (B) `klt1` or `Kgt9` (C) `1ltklt9` (D) none of these

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

The inverse of the point (1, 2) with respect to the circle x^(2) + y^(2) - 4x - 6y + 9 = 0 is

The point on the parabola 4x=y^2 + 9-6y which is closest to the circle x^2 + y^2 - 10x - 10y + 49 = 0 is: (A) (9/4, 0) (B) (4, 11) (C) (1, 1) (D) none of these

If the line y = mx - (m-1) cuts the circle x^2+y^2=4 at two real and distinct points then total values of m are

The line x + 2y = a intersects the circle x^2 + y^2 = 4 at two distinct points A and B Another line 12x - 6y - 41 = 0 intersects the circle x^2 + y^2 - 4x - 2y + 1 = 0 at two C and D . The value of 'a' for which the points A,B,C and D are concyclic -

If int_0^1 xe^(x^2) dx=k int_0^1 e^(x^2) dx , then (A) kgt1 (B) 0ltklt1 (C) k=1 (D) none of these

The line x=t^2 meets the ellipse x^2+(y^2)/9=1 at real and distinct points if and only if. |t|<2 (b) |t|<1 |t|>1 (d) none of these

The curve x y=c ,(c >0), and the circle x^2+y^2=1 touch at two points. Then the distance between the point of contacts is 1 (b) 2 (c) 2sqrt(2) (d) none of these

The line x+2y=1 cuts the ellipse x^(2)+4y^(2)=1 1 at two distinct points A and B. Point C is on the ellipse such that area of triangle ABC is maximum, then find point C.

Find the equation of the circle concentric with the circle x^2 +y^2 - 4x - 6y-9=0 and passing through the point (-4, -5)