Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the eccentric angles of the extremities of the latus recta of the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$

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A tangent is drawn to each of the circles $x_{2}+y_{2}=a_{2}$ and $x_{2}+y_{2}=b_{2}˙$ Show that if the two tangents are mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.

If real numbers $xandy$ satisfy $(x+5)_{2}+(y−12)_{2}=(14)_{2},$ then the minimum value of $x_{2}+y_{2} $ is_________

$AandB$ are two points in the xy-plane, which are $22 $ units distance apart and subtend an angle of $90_{0}$ at the point $C(1,2)$ on the line $x−y+1=0$ , which is larger than any angle subtended by the line segment $AB$ at any other point on the line. Find the equation(s) of the circle through the points $A,BandC˙$

An infinite number of tangents can be drawn from $(1,2)$ to the circle $x_{2}+y_{2}−2x−4y+λ=0$ . Then find the value of $λ$

Find the equations of the circles passing through the point $(−4,3)$ and touching the lines $x+y=2$ and $x−y=2$

Find the equation of the tangent at the endpoints of the diameter of circle $(x−a)_{2}+(y−b)_{2}=r_{2}$ which is inclined at an angle $θ$ with the positive x-axis.

Two circles $C_{1}$ and $C_{2}$ intersect in such a way that their common chord is of maximum length. The center of $C_{1}$ is (1, 2) and its radius is 3 units. The radius of $C_{2}$ is 5 units. If the slope of the common chord is $43 ,$ then find the center of $C_{2}˙$

Two circles $C_{1}andC_{2}$ intersect at two distinct points $PandQ$ in a line passing through $P$ meets circles $C_{1}andC_{2}$ at $AandB$ , respectively. Let $Y$ be the midpoint of $AB,andQY$ meets circles $C_{1}andC_{2}$ at $XandZ$ , respectively. Then prove that $Y$ is the midpoint of $XZ˙$