AB is a chord of x2+y2=4 and P(1,1) trisects AB. Then the length of the chord AB is
Let Sbe the circle in the xy-plane defined by the equation x2+y2=4.(For Ques. No 15 and 16)Let Pbe a point on the circle Swith both coordinates being positive. Let the tangent to Sat Pintersect the coordinate axes at the points Mand N. Then, the mid-point of the line segment MNmust lie on the curve(x+y)2=3xy(b) x2/3+y2/3=24/3(c) x2+y2=2xy(d) x2+y2=x2y2
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 x2+y2=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 x2+y2=4 and x2+y2−2x+6y+1=0 is