Circles practice · Easy

The locus of the foot of perpendicular drawn from the centre of the ellipse ${x^2} + 3{y^2} = 6$ on any tangent to it is

The points $\left( {5, - 7} \right)$ lies outside the circle

The locus of a point which moves so that the ratio of the length of the tangents to the circles ${x^2} + {y^2} + 4x + 3 = 0$ and ${x^2} + {y^2} - 6x + 5 = 0$ is $2:3$, is

The range of values of $\theta \in \left[ {0,2\pi } \right]$ for which $\left( {1 + \cos \theta ,\sin \theta } \right)$ is on interior point of the circle ${x^2} + {y^2} = 1,$ is

The equation of circle which touches the line $x+3 y-2=0$ and $3 x+9 y-2=0$, also the point of contact on first line is $(-1,1)$, is

Length of the common chord of the circles $(x-1)^2+(y+1)^2=c^2$ and $(x+1)^2+(y-1)^2=c^2$ is

The tangent to ${x^2} + {y^2} = 9$ which is parallel to $y - axis$ and does not lie in the third quadrant touches the circle at the point

The locus of a point which moves such that the sum of the squares of its distances from three vertices of a triangle is a circle whose centre is at the

If the points $(0,0),(1,0),(0,1)$ and $(t, t)$ are concyclic, then $t=$

The locus of the centre of a circle which touches externally the circle $x^2+y^2-6 x-6 y+14=0$ and also touches $Y$-axis, is given by the equation

The equation of the circle passing through $(1,0)$ and $(0,1)$ and having the smallest possible radius, is

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

The set of values of a for which the point $(2 a, a+1)$ is an interior point of the larger segment of the circle $x^2+y^2-2 x-2 y-8=0$ made by the chord $x-y+1=0$, is

The normal at the point $\left( {3,4} \right)$ on a circle at the point $\left( { - 1, - 2} \right).$ The equation of the circle, is

If the line $y-m x+m-1=0$ cuts the circle $x^2+y^2-4 x-4 y+4$ $=0$ at two real points, then $m$ belongs to

If the circles ${\left( {x - a} \right)^2} + {\left( {y - b} \right)^2} = {c^2}$ and ${\left( {x - b} \right)^2} + {\left( {y - a} \right)^2} = {c^2}$ touch each other, then

The circles ${x^2} + {y^2} - 8x + 4y + 4 = 0$ touches

The equation $x^2+y^2-6 x+8 y+25=0$ represents

The equation of the locus of the middle point of a chord of the circle $x^2+y^2-2 x-2 y=0$ 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

The number of common tangents of the circles given by $x^{2}+y^{2}-8 x-2 y+1=0$ and $x^{2}+y^{2}+6 x+8 y=0$ is

The condition for a line $y = 2x + c$ to touch the circle ${x^2} + {y^2} = 16$ is

The circle ${x^2} + {y^2} - 3x - 4y + 2 = 0$ cuts $x$-axis at

If $5x - 12y + 10 = 0$ and $12y - 5x + 16 = 0$ are two tangents to a circle, the radius of the circle is

If the area of the circle $4{x^2} + 4{y^2} - 8x + 16y + k = 0$ is $9\pi$ sq unit, then the value of $k$ is

If two circles $x^2+y^2+2 g x+2 f y=0$ and $x^2+y^2+2 g_1 x+2 f_1 y=0$ touch each other, then

Suppose $f(x, y)=0$ is the equation of a circle such that $f(x, 1)=0$ has equal roots (each equal to 2) and $f(1, x)=0$ also has equal roots (each equal to zero). The equation of circle is

An equation of the circle described on the chord $x \cos \alpha+y \sin \alpha-p=0$ of the circle $x^2+y^2=a^2$ as diameter is

The smallest circle with centre on y-axis and passing through the point(7,3)has radius

Consider four circles $(x \pm 1)^2+(y \pm 1)^2=1$. Equation of smaller circle touching these four circles is

The circle $x^2+y^2=4 x+8 y+5$ intersects the line $3 x-4 y=m$ at two distinct points, if