Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the locus of the middle points of all chords of $4x_{2} +9y_{2} =1$ which are at a distance of 2 units from the vertex of parabola $y_{2}=−8ax˙$

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The range of parameter $_{′}a_{′}$ for which the variable line $y=2x+a$ lies between the circles $x_{2}+y_{2}−2x−2y+1=0$ and $x_{2}+y_{2}−16x−2y+61=0$ without intersecting or touching either circle is $a∈(25 −15,0)$ $a∈(−∞,25 −15,)$ $a∈(0,−5 −1)$ (d) $a∈(−5 −1,∞)$

Find the length of the common chord of the circles $x_{2}+y_{2}+2x+6y=0$ and $x_{2}+y_{2}−4x−2y−6=0$

The chords of contact of tangents from three points $A,BandC$ to the circle $x_{2}+y_{2}=a_{2}$ are concurrent. Then $A,BandC$ will (a)be concyclic (b) be collinear (c)form the vertices of a triangle (d)none of these

If the lines $x+y=6andx+2y=4$ are diameters of the circle which passes through the point (2, 6), then find its equation.

$C_{1}$ and $C_{2}$ are circle of unit radius with centers at (0, 0) and (1, 0), respectively, $C_{3}$ is a circle of unit radius. It passes through the centers of the circles $C_{1}andC_{2}$ and has its center above the x-axis. Find the equation of the common tangent to $C_{1}andC_{3}$ which does not pass through $C_{2}˙$

Consider the circles $x_{2}+(y−1)_{2}=9,(x−1)_{2}+y_{2}=25.$ They are such that these circles touch each other one of these circles lies entirely inside the other each of these circles lies outside the other they intersect at two points.

Find the angle between the two tangents from the origin to the circle $(x−7)_{2}+(y+1)_{2}=25$

Find the locus of the center of the circle which cuts off intercepts of lengths $2aand2b$ from the x-and the y-axis, respectively.