A circle with center `(a , b)` passes through the origin. The equation of the tangent to the circle at the origin is (a)`a x-b y=0` (b) `a x+b y=0` (c)`b x-a y=0` (d) `b x+a y=0`

The equations of tangents to the circle x^2+y^2-6x-6y+9=0 drawn from the origin in (a) x=0 (b) x=y (c) y=0 (d) x+y=0

The equation of the tangent to the circle x^2+y^2=25 passing through (-2,11) is (a) 4x+3y=25 (b) 3x+4y=38 (c) 24 x-7y+125=0 (d) 7x+24 y=250

The equation of tangent to hyperbola 4x^2-5y^2=20 which is parallel to x-y=2 is (a) x-y+3=0 (b) x-y+1=0 (c) x-y=0 (d) x-y-3=0

If 3x+y=0 is a tangent to a circle whose center is (2,-1) , then find the equation of the other tangent to the circle from the origin.

The equation of the tangent tothe curve y={x^2 sin(1/x),x!=0 and 0, x=0 at the origin is

The equation of the tangent to the curve y=b e^(-x//a) at the point where it crosses the y-axis is a)x/a-y/b=1 (b) a x+b y=1 c)a x-b y=1 (d) x/a+y/b=1

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

The asymptotes of the hyperbola x y=h x+k y are (a) x-k=0 and y-h=0 (b) x+h=0 and y+k=0 (c) x-k=0 and y+h=0 (d) x+k=0 and y-h=0

The equation of the plane through the intersection of the planes x+2y+3z-4=0 and 4x+3y+2z+1=0 and passing through the origin is (a) 17x+14y+11z=0 (b) 7x+4y+z=0 (c) x+14+11z=0 (d) 17x+y+z=0

The equation of the line passing through the origin and the point of intersection of the lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 is