Question

12.If the centre of a circle is (2a, a – 7), then Find the values of a, if the circle passes

through the point (11, – 9) and has diameter 10√2 units. (4)

13. State and prove Pythagoras theorem.​

Answer 1

Step-by-step explanation:

distance between centre and any point on circumference is radius of circle. hence, using distance formula

(2a-11)^2 + ((a-7-(-9))^2 = (10√2)^2

4a^2 +121 -44a + (a+2)^2 = 100*2

4a^2 +121-44a+a^2+4+4a.= 200

5a^2 - 40a + 125-200 = 0

5a^2 - 40a - 75 = 0

a^2 - 8a - 15 = 0

x = -(-8)+_√(-8)^2 - 4**1*(-15)/2*1

= 8 +_√(64+60)/2

= 8+_√124/2

= 8+_2√31/2

= 4+_√31

x= 4+√31 and 4-√31