Circle · Mathematics · AP EAPCET

The locus of mid-points of points of intersection of $$x \cos \theta+y \sin \theta=1$$ with the coordinate axes is

The radius of the circle having. $$3 x-4 y+4=0$$ and $$6 x-8 y-7=0$$ as its tangents is

A circle is such that $$(x-2) \cos \theta+(y-2) \sin \theta=1$$ touches it for all values of $$\theta$$. Then, the circle is

The least distance of the point $$(10,7)$$ from the circle $$x^2+y^2-4 x-2 y-20=0$$ is

Suppose that the $$x$$-coordinates of the points $$A$$ and $$B$$ satisfy $$x^2+2 x-a^2=0$$ and their $$y$$-coordinates satisfy $$y^2+4 y-b^2=0$$. Then, the equation of the circle with $$A B$$ as its diameter is

The radical centre of the three circles $$x^2+y^2-1=0, x^2+y^2-8 x+15=0$$ and $$x^2+y^2+10 y+24=0$$ is

For any real number $$t$$, the point $$\left(\frac{8 t}{1+t^2}, \frac{4\left(1-t^2\right)}{1+t^2}\right)$$ lies on a / an

The area of the circle passing through the points $$(5, \pm 2),(1,2)$$ is

The ratio of the largest and shortest distances from the point $$(2,-7)$$ to the circle $$x^2+y^2-14 x-10 y-151=0$$ is

A circle has its centre in the first quadrant and passes through $$(2,3)$$. If this circle makes intercepts of length 3 and 4 respectively on $$x=2$$ and $$y=3$$, its equation is

The image of the point $$(3,4)$$ with respect to the radical axis of the circles $$x^2+y^2+8 x+2 y+10=0$$ and $$x^2+y^2+7 x+3 y+10=0$$ is

The locus of centers of the circles, possessing the same area and having $$3 x-4 y+4=0$$ and $$6 x-8 y-7=0$$ as their common tangent, is

For any two non-zero real numbers $$a$$ and $$b$$ if this line $$\frac{x}{a}+\frac{y}{b}=1$$ is a tangent to the circle $$x^2+y^2=1$$, then which of the following is true?

The length of the intercept on the line $$4 x-3 y-10=0$$ by the circle $$x^2+y^2-2 x+4 y-20=0$$ is

The pole of the line $$\frac{x}{a}+\frac{y}{b}=1$$ with respect to the circle $$x^2+y^2=c^2$$ is

If the tangent at the point $$P$$ on the circle $$x^2+y^2+6 x+6 y=2$$ meets the straight line $$5 x-2 y+6=0$$ at a point $$Q$$ on the $$Y$$-axis, then the length of $$P Q$$ is

The locus of a point, which is at a distance of 4 units from $$(3,-2)$$ in $$x y$$-plane is

Find the equation of the circle which passes through origin and cuts off the intercepts $$-$$2 and 3 over the $$X$$ and $$Y$$-axes respectively.

The angle between the pair of tangents drawn from $$(1,1)$$ to the circle $$x^2+y^2+4 x+4 y-1=0$$ is

If the circle $$x^2+y^2-4 x-8 y-5=0$$ intersects the line $$3 x-4 y-m=0$$ in two distinct points, then the number of integral values of '$$m$$' is

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

The length of the common chord of the circles $$x^2+y^2+3x+5y+4=0$$ and $$x^2+y^2+5x+3y+4=0$$ is __________ units.

Find the equation of the circle which passes through the point $$(1,2)$$ and the points of intersection of the circles $$x^2+y^2-8 x-6 y+21=0$$ and $$x^2+y^2-2 x-15=0$$

Given, two fixed points $$A(-2,1)$$ and $$B(3,0)$$. Find the locus of a point $$P$$ which moves such that the angle $$\angle A P B$$ is always a right angle.

The equations of the tangents to the circle $$x^2+y^2=4$$ drawn from the point $$(4,0)$$ are

If $$P(-9,-1)$$ is a point on the circle $$x^2+y^2+4 x+8 y-38=0$$, then find equation of the tangent drawn at the other end of the diameter drawn through $$P$$

Find the equation of a circle whose radius is 5 units and passes through two points on the $$X$$-axis, which are at a distance of 4 units from the origin

If a foot of the normal from the point $$(4,3)$$ to a circle is $$(2,1)$$ and $$2 x-y-2=0$$, is a diameter of the circle, then the equation of circle is

The length of the tangent from any point on the circle $$(x-3)^2+(y+2)^2=5 r^2$$ to the circle $$(x-3)^2+(y+2)^2=r^2$$ is 16 units, then the area between the two circles in square units is

The equation of the circle, which cuts orthogonally each of the three circles

$$\begin{aligned} & x^2+y^2-2 x+3 y-7=0, \\ & x^2+y^2+5 x-5 y+9=0 \text { and } \\ & x^2+y^2+7 x-9 y+29=0 \end{aligned}$$

Find the equations of the tangents drawn to the circle $$x^2+y^2=50$$ at the points where the line $$x+7=0$$ meets it.

If the chord of contact of tangents from a point on the circle $$x^2+y^2=r_1^2$$ to the circle $$x^2+y^2=r_2^2$$ touches the circle $$x^2+y^2=r_3^2$$, then $$r_1, r_2$$ and $$r_3$$ are in

Find the equation of the circle passing through $$(1,-2)$$ and touching the $$X$$-axis at $$(3,0)$$.

Let $$L_1$$ be a straight line passing through the origin and $$L_2$$ be the straight line $$x+y=1$$. If the intercepts made by the circle $$x^2+y^2-x+3 y=0$$ on $$L_1$$ and $$L_2$$ are equal, then which of the following equations represent $$L_1$$

The radius of the circle whose center lies at $$(1,2)$$ while cutting the circle $$x^2+y^2+4 x+16 y-30=0$$ orthogonally, is units.

The point which has the same power with respect to each of the circles $$x^2+y^2-8 x+40=0, x^2+y^2-5 x+16=0$$ and $$x^2+y^2-8 x+16 y+160=0$$ is