A.Maths answers on Circles

Circles

Section A

1. x² + y² - 2x - 17  =  0

2. x² + y² + 2x + 2y - 2  =  0

3. x² + y² - 6x - 2y + 5  =  0

4. x² + y² - 3x - 2 = 0

5. 2x + y - 1 = 0  and  2x + y + 19 = 0

6. 4*(square root of 5)

7. y=0 or y=(4/3)x

8. a) prove

    b) 3x - y - 15   =  0

9. a) (k² - 1)x² + (k² - 1)y² + 4x - 12k²y + 12k² - 4 = 0

    b) x - 3y + 8  =  0   which is a straight line

    c) When k ¹ 1, the locus is a circle.

10.a) centre=(5,0)  radius=3

    b) m= (square root of 2)/2 or -(square root of 2)/2

11.  5x² + 5y² - 26x - 4y + 22 = 0

12. x - 2y = 0   or   7x + 7y - 9 = 0  or   x + y - 3 = 0

Section B

1. a) R=(-7,0)

    b) x² + y² + 7x - y = 0

    c) 5

    d) (10*(square root of 7))/3

2. a) 2

    b) (4*(square root of 3))/3

        Area of BCD= (32/ (1-r) )- (32r/ (1+r)² )

    c) B=((27+8*square root of 3)/15, (3+2*square root of 3)/5)

        C=((27-8*square root of 3)/15, (3-2*square root of 3)/5)

3. a) Centre=(2,-1)  Radius=2

    b) Prove

    c) x+y-3=0

    d) x² + y² - 4x + 2y + 1 +k(x + y - 3) = 0.

    e) 3x² + 3y² - 11x + 7y =  0

4. a) centre of C₁ = (-6, 3)   radius of C₁  = 5

           centre of C₂  =(6, -6)   radius of C₂  = 10

            Prove

    b) (i) 4x - 3y + 8 = 0

       (ii)  (-2,0)