c1 maths question? Coordinate geometry

12 A circle has equation (x − 2)2 + y2 = 20.

(i) Write down the radius of the circle and the coordinates of its centre. [2]

(ii) Find the points of intersection of the circle with the y-axis and sketch the circle. [3]

(iii) Show that, where the line y = 2x + k intersects the circle, 5x2 + (4k − 4) x + k2 − 16 = 0. [3]

(iv) Hence find the values of k for which the line y = 2x + k is a tangent to the circle.

Managed to get all but iv which im really confused by, can anyone help? I know its to do with b^2-4ac but i dont know how you do it

if you have done part iii, then if the line is a tangent you are looking for repeated roots from the quadratic of part iii

Hello, friend

Since you seem like a knowledgeable lad, is the coordinate of the centre (2,0)?

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Yes

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Thanks mate

I was confused about the y-coordiante because the equation of the circle has only a y^2

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