What are the Answers to all theses questions?

A(5, 5) and B(7, 10) are houses and y = 8 is a gas pipeline. Where should the one outlet from the pipeline be placed so that it is the same distance from both houses? (CD) is a water pipeline. A and B are two towns. A pumping station is to be located on the pipeline to pump water to A and B. Each town is to pay for their own service pipes and they insist on equality of costs. a Where shOuld C be located to ensure equality of costs? It What is the total length of service pipe required? I: If the towns agree to pay equal amounts, would it be cheaper to install the service pipeline om D to B to A? A(2, 3) EU, 10) o y: 8 o A(5,5) C D ........................................................................ y:7 B(5,4) Scale: 1 unit E 1 km 20 y Jason's girliend lives in a house on Clifton I'llghway Highway which has equation y = 8. The distance 'as the crow ies' from Jason's house to his girl-iend's house is 11.73 km. If Jason lives at (4, 1), what are the coordinates of his girliend's house? || 00 .59 'Ee 8 1(4, 1) Scale: 1 unit E 1 km. 21 a A circle has centre (a, b) and radius r units. P(;c, y) moves on the circle. Show that (:1: a)2 + (y b)2 = r2. b Find the equation of the circle with: i centre (4, 3) and radius 5 units ii centre (1, 5) and radius 2 units iii centre (0, 0) and radius 10 units ill ends of a diameter (1, 5) and (3, 1). 22 Find the centre and radius of the circle: a (at1)2+(y3)2=4 b 32+(y+2)2=16 c m2+y2= 23 Consider the circle with equation (:1: 2)2 + (y + 3)2 = 20. a State the circle's centre and radius. b Show that (4, 1) lies on the circle. c Find the equation of the tangent to the circle at the point (4, 1). 24 The perpendicular bisector of a chord of a circle passes through the centre of the circle. Find the centre of a circle passing through points P(5, 7), Q(7, 1) and R(1, 5) by nding the \" perpendicular bisectors of [PQ] and [QR] and ' solving them simultaneously