The point D, E and F have coordinates (-2,0), (0,-1) and (2,3) respectively.

i) gradient of DE = -0.5

ii) 0.5x+y-4=0 line F parallel to DE

iii) by calculating the gradient of EF, show that DEF is a right-angled triangle.

iv) calculate the length of DF.

v) Use the results of parts(iii) and (iv to show that the circle which passes through D,E and F has equation $\displaystyle x^2+y^2-3y-4=0.$

i've done i),ii),iii),iv)

i) gradient of DE = -0.5

ii) 0.5x+y-4=0 line F parallel to DE

iii) y= 2x-1 = grad of normal

y=-0.5 = grad of tangent

which bisect DE at some point therefore it's a right angled triangle.

iv) $\displaystyle sqroot(4^2+3^2)$

thank you for helping!