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 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

The distance of the straight line a(x-a)+b(y-b)=0 from the origin is -

The point of intersection of the tangents of the parabola y^2=4x drawn at the endpoints of the chord x+y=2 lies on (a) x-2y=0 (b) x+2y=0 (c) y-x=0 (d) x+y=0

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is (a) x+y=2 (b) x-y=2 (c) 2x-y=1 (d) none of these

A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0)(beta,0) both to the right of the origin. A circle also passes through these two points. The length of a tangent from the origin to the circle is: (a) sqrt((b c)/a) (b) a c^2 (c) b/a (d) sqrt(c/a)

If O Aa n dO B are equal perpendicular chords of the circles x^2+y^2-2x+4y=0 , then the equations of O Aa n dO B are, where O is the origin. (a) 3x+y=0 and 3x-y=0 (b) 3x+y=0 and 3y-x=0 (c) x+3y=0 and y-3x=0 (d) x+y=0 and x-y=0