Class 12

Math

Co-ordinate Geometry

Circles

AB is a chord of $x_{2}+y_{2}=4$ and $P(1,1)$ trisects AB. Then the length of the chord AB is

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Let $S$be the circle in the $xy$-plane defined by the equation $x_{2}+y_{2}=4.$(For Ques. No 15 and 16)Let $P$be a point on the circle $S$with both coordinates being positive. Let the tangent to $S$at $P$intersect the coordinate axes at the points $M$and $N$. Then, the mid-point of the line segment $MN$must lie on the curve$(x+y)_{2}=3xy$(b) $x_{2/3}+y_{2/3}=2_{4/3}$(c) $x_{2}+y_{2}=2xy$(d) $x_{2}+y_{2}=x_{2}y_{2}$

P and Q are two points on a line passing through (2,4) and having slope m. if a line segment AB subtends a right angles at P and Q, where $A≡(0,0)$ and $B≡(6,0)$ , then range of values of m is

If a line intersects two concentric circles (circles with the same centre) with centre $O$ at $A,B,C$ and $D$, prove that $AB=CD$ (see figure)

PA and PB are tangents to a circle S touching it at points A and B. C is a point on S in between A and B as shown in the figure. LCM is a tangent to S intersecting PA and PB in points L and M, respectively. Then the perimeter of the triangle PLM depends on

Tangents drawn from point of intersection A of circles $x_{2}+y_{2}=4$ and $(x−3 )_{2}+(y−3)_{2}=4$ cut the line joining their centres at B and C then triangle BAC is

Write true or false: Give reasons for your answers.(1) Line segment joining the centre to any point on the circle is a radius of the circle.(2) A circle has only finite number of equal chords.(3) If a circle is divided into three equal arcs, each is a major arc.(4) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.(5) Sector is the region between the chord and its corresponding arc.(6) A circle is a plane figure.

The locus of the centre of the circle which bisects the circumferences of the circles $x_{2}+y_{2}=4$ and $x_{2}+y_{2}−2x+6y+1=0$ is

An isosceles triangle with base 24 and legs 15 each is inscribed in a circle with centre at $(−1,1)$. The locus of the centroid of that $Δ$ is