Variation

Drag the diagrams to the appropriate colour boxes below, then press the "Submit" button.

 

 

 

 
y is partly constant and partly varies inversely as x. y varies inversely as x. y is partly constant and partly varies as x. y varies directly as x.


 

 

 

Coordinate Geometry

1. The circles C:x2+y2=4 and C' are symmetrical about the line x+y=4. Find the equation of C'.
x2+y2-8x-8y+28=0
 x2+y2+8x+8y+8=0
 x2+y2-8x-8y-12=0
 x2+y2-4x-4y-8=0

 

2. Which of the following statement(s) about the circle C : (x-a)2+(y+b)2=a2+b2 is/are true?

(I) C passes through the origin

(II)C is divided by the line x + y = a - b into 2 equal parts

(III)The centre of C lies in Quadrant IV

I only
 I and III only
 II and III only
 I and II only

 

3. Which of the following circle(s) does/do not meet the line x=a, where a>b>0?

I.(x+a)2+y2=3a2+b2 II. (x-2a)2+y2=a2+b2 III.x2+(y+b)2=a2?

I only
 II only
 II and III only
 I and III only

 

4. The area of the circle 2x2+2y2+4x+(2-k)=0 is3pi. Find the value of k.
3
 6
 square root of 3
 square root of 6

5. How many common tangents to exactly 2 circles at a time are there in the given diagram?

6
 7
 8
 9
6.For each of the following, choose one of the diagrams on the right that best describes the relative positions of C and C' on the left and drag it to the corresponding coloured box . (Hint: find the distance between the centres of each pair of circles.) Press the "Submit" button to check the answer.
(a) circle centre radius
  C (3,7) 4
  C' (-2,-5) 9
     
(b) circle centre radius
  C (3,7) 5
  C' (-2,-5) 6
     
(c) circle centre radius
  C (3,7) 6
  C' (-1,4) 2
     
(d) circle centre radius
  C (3,7) 3
  C' (-1,4) 8

 

      
(e) circle centre radius
  C (3,7) 5
  C' (-1,4) 12
     

7.Which of the following graphs represent the line ax+by+c=0 where a<0, b>0 and c<0?
 

(Full mark 110)