Circle — JEE Main PYQs

The circle passing through $(1,-2)$ and touching the axis of x at $(3,0)$ also passes through the point

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, and having centre at $(0,3)$ is

The length of the diameter of the circle which touches the $x$-axis at the point $(1,0)$ and passes through the point $(2,3)$ is

The two circles $x^2+y^2=ax$ and $x^2+y^2=c^2(c>0)$ touch each other if

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

If $P$ and $Q$ are the points of intersection of the circles $x^2+y^2+3x+7y+2p-5=0$ and $x^2+y^2+2x+2y-p^2=0$, then there is a circle passing through $P,Q$ and $(1,1)$ for

Three distinct points $\mathrm{A},\mathrm{B}$ and C are given in the $2-$ dimensional coordinate plane such that the ratio of the distance of any one of them from the point ( 1,0 ) to the distance from the point ( $-1,0$ ) is equal to $\frac{1}{3}$. Then the circumcentre …

The point diametrically opposite to the point $P(1,0)$ on the circle $x^2+y^2+2x+4y-3=0$ is

Consider a family of circles which are passing through the point $(-1,1)$ and are tangent to $x$ axis. If $(h,k)$ are the co-ordinates of the centre of the circles, then the set of values of $k$ is given by the interval

If the lines $3x-4y-7=0$ and $2x-3y-5=0$ are two diameters of a circle of area $49\pi$ square units, the equation of the circle is

Let C be the circle with centre $(0,0)$ and radius 3 units. The equation of the locus of the mid points of the chords of the circle $C$ that subtend an angle of $\frac{2\pi }{3}$ at its centre is

If the circles $x^2+y^2+2ax+cy+a=0$ and $x^2+y^2-3ax+dy-1=0$ intersect in two distinct points P and Q then the line $5x+by-a=0$ passes through P and Q for

If a circle passes through the point $(a,b)$ and cuts the circle $x^2+y^2=p^2$ orthogonally, then the equation of the locus of its centre is

If a circle passes through the point $(a,b)$ and cuts the circle $x^2+y^2=4$ orthogonally, then the locus of its centre is

If the lines $2x+3y+1=0$ and $3x-y-4=0$ lie along diameters of a circle of circumference $10\pi$, then the equation of the circle is

The intercept on the line $\mathrm{y}=\mathrm{x}$ by the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-2\mathrm{x}=0$ is AB . Equation of the circle on AB as a diameter is