The area of the quadrilateral formed by the tangents from the point (4,5) to the circle x²+y²-4x-2y-11=0 with a pair of radii joining the points of contact of these tangents is

The equation of the normal to the curve (x/a)^2/3+(y/b)^2/3=1 at (a cos³θ, b sin³θ ) is

The distance between the limiting points of the coaxial system x² + y² – 4x – 2y – 4 + 2λ(3x + 4y + 10)=0

The condition that the pair of tangents drawn from the origin to the circle x²+y²+2gx+2fy+c=0 may be at right angles is

The equation of the chord of the circle x²+y²+16x+2y+10=0 parallel to the chord x-3y-15=0 and which is at the same distance from the centre is

If the tangent to the circle x²+y²=5 at (1, -2) also touches the circle x²+y²-8x+6y+20=0, then the point of contact is

The radical centre of the circle x²+y²+a_rx+b_r y+c=0, r=1, 2, 3 is

The equation of the circle cutting the circle x²+y²+2x-4y+8=0 orthogonally and coaxial with the circle x²+y²+6x-4y-12=0, x²+y²-4x-6y-12=0 is

The inverse point of (1, -1) with resapect to the circle x²+y²=4 is

The equation of the tangent to the circle x²+y²+2x+2y-7=0 which makes 45⁰ with the x axis is