Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the equation of chord of an ellipse $25x_{2} +16y_{2} =1$ joining two points $P(3π )andQ(6π )$

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Find the center of the circle $x=−1+2cosθ,y=3+2sinθ$

If the intercepts of the variable circle on the x- and yl-axis are 2 units and 4 units, respectively, then find the locus of the center of the variable circle.

Find the locus of the midpoint of the chord of the circle $x_{2}+y_{2}−2x−2y=0$ , which makes an angle of $120_{0}$ at the center.

Let $P$ be a point on the circle $x_{2}+y_{2}=9,Q$ a point on the line $7x+y+3=0$ , and the perpendicular bisector of $PQ$ be the line $x−y+1=0$ . Then the coordinates of $P$ are $(0,−3)$ (b) $(0,3)$ $(2572 ,3521 )$ (d) $(−2572 ,2521 )$

Statement 1 :The circles $x_{2}+y_{2}+2px+r=0$ and $x_{2}+y_{2}+2qy+r=0$ touch if $p_{2}1 +q_{2}1 =e1 ˙$ Statement 2 : Two centers $C_{1}andC_{2}$ and radii $r_{1}andr_{2},$ respectively, touch each other if $∣r_{1}±r_{2}∣=c_{1}c_{2}˙$

Find the length of the chord of contact with respect to the point on the director circle of circle $x_{2}+y_{2}+2ax−2by+a_{2}−b_{2}=0$ .

Consider three circles $C_{1},C_{2}andC_{3}$ such that $C_{2}$ is the director circle of $C_{1},andC_{3}$ is the director circlÃ© of $C_{2}$. Tangents to $C_{1}$, from any point on $C_{3}$ intersect $C_{2}$, at $P_{2}andQ$. Find the angle between the tangents to $C_{2}$ at P and Q. Also identify the locus of the point of intersec- tion of tangents at $PandQ$.

Find the equation of the small circle that touches the circle $x_{2}+y_{2}=1$ and passes through the point $(4,3)˙$