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# Q4 c1 is the circle x² + y² -4y-20=0 and l is the line 2x-y+5=0

Q4 c1 is the circle x² + y² -4y-20=0 and l is the line 2x-y+5=0

(a) write down the centre and radius lenght of c1

(b) Find the perpendicular distance from the centre of c1 to the line l in surd form

(ii) Hence or otherwise find PQ in surd form

(c) PQ is the diameter of circle c2
Find the equation of c2

### 1 Answer by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
1
X^2 + Y^2 - 4y -20 =0

X^2 + Y^2 - 4Y +4 = 24

X^2 + ( Y - 2 ) ^2 = 24

c1 : ( 0 , 2)

b)   L1 : 2X - y + 5 = 0

L2  :   Y = -1/2 X +b

2 = -1/2 (0) +b

L2 :  Y = -1/2 X + 2

L1 :     2X - Y = -5
L2       1/2X+ Y = 2

5/ 2 X = -3

X = - 6/5      Y = 13/5

PQ :   ( 0, 2 ) ( -6/5 , 13/5)

d =√( ( -6/5 -0) ^2 ) + ( 13/5 - 2 ) ^2 )=

=  √ ( 36/ 25) + ( 9/ 25) = √(45)/ 5 = 3√5/ 5

c ) :

( 0, 2 )   ( -6/5 , 13/5)

m = ( 13/5  - 2 ) / ( -6/5 - 0) = - 1/2

Y = -1/2 X + b

2 = -1/2(0) + b   , b= 2

Y = - 1/2 X + 2