Circle - Coordinate Geometry | Mathematics PYQ

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 \(P\)

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

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 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

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 equation of the pair of straight lines parallel to \(x\)-axis and touching the circle \(x^2+y^2-6 x-4 y-12=0\) is

The center and radius of the circle \(x^2+y^2+8 x+10 y-8=0\) respectively are and units

The points where the circle \(x^2+y^2-3 x -4 y+2=0\) cuts the \(X\)-axis are

The poles of the tangents to the circle \(x^2+y^2=4\) with respect to the circle \((x+2)^2+y^2=8\), lie on

If the power of the point \((1,6)\) with respect to the circle \(x^2+y^2+4 x-6 y-a=0\) is \(-16\) then \(a\) equals

The equation of radical axis of the circles \(x^2+y^2+4 x+6 y+7=0\) and \(4 x^2+4 y^2+8 x+12 y-9=0\) is

The radical axis of the circles \(S_1: x^2+y^2-4 x+6 y-10=0\) and \(S_2 : x^2+y^2+2 x-6 y+2=0\), cut the circle \(S_1\) in