Using Algebra show that part of the line 3x + 4y = 0 is a diameter of the circle with equation (x^2) + (y^2) = 25
To show that the line is a diameter of the circle you muct show that it goes through the centre of the circle1) finding the centre of the circle. The general eqn is (x-a)2 + (y-b)2 = r2 , where r is the radius and (a, b) is the centre
to get x2 + y2 = 25 , centre must be the origin -> (x-0)2 + (y -0)2 = 25 x2 - 0x + 0 + y2 -0y + 0 = x2 + y2
2) then to prove it goes through line, sub (0, 0) into line equation 3x + 4y =0 -> (3x0) + (4x0) = 0
the line 3x + 4y = 0 goes through the centre of the circle and therefore must be a diameter
EL
