If the angle between the tangents drawn to `x^2+y^2+2gx+2fy+c=0` from (0, 0) is `pi/2,` then (a) `g^2+f^2=3c` (b) `g^2+f^2=2c` (c) `g^2+f^2=5c` (d) `g^2+f^2=4c`

The angle between the tangents to the curve y=x^2-5x+6 at the point (2, 0) and (3, 0) is pi/2 (b) pi/3 (c) pi (d) pi/4

The distance between the chords of contact of tangents to the circle x^2+y^2+2gx +2fy+c=0 from the origin & the point (g,f) is

Find the length of the tangent drawn from any point on the circle x^2+y^2+2gx+2fy+c_1=0 to the circle x^2+y^2+2gx+2fy+c_2=0

The equation x^(2) + y^(2) + 2gx + 2fy + c=0 reprsents the circle if

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

If from any point P on the circle x^2+y^2+2gx+2fy+c=0, tangents are drawn to the circle x^2+y^2+2gx+2fy+csin^2alpha+(g^2+f^2)cos^2alpha=0 , then find the angle between the tangents.

Statement 1 : The circle having equation x^2+y^2-2x+6y+5=0 intersects both the coordinate axes. Statement 2 : The lengths of xa n dy intercepts made by the circle having equation x^2+y^2+2gx+2fy+c=0 are 2sqrt(g^2-c) and 2sqrt(f^2-c) , respectively.

If the equation x^2+y^2+2h x y+2gx+2fy+c=0 represents a circle, then the condition for that circle to pass through three quadrants only but not passing through the origin is (a) f^2> c (b) g^2>2 (c) c >0 (d) h=0