The two tangent points are equidistant from the circle's centre.

Recall the circle property : tangent is perpendicular to radius

So vertical distance from centre to x-axis = horizontal distance from centre to y-axis

(i.e the two distances are basically the radii of the circle)

Let this radius be r, and then use Pythagoras' Theorem to solve for r.

(ii)

Since r = 4, it is pretty obvious what the coordinates of the centre are (use the fact that the tangent points are equidistant from centre)

Circle equation (standard form) :

(x - a)² + (y - b)² = r²

(a,b) are the coordinates of the centre

(iii) once you know the centre of C1,

Then you just have mirror this centre about the line x = 5 to find the centre of C2.

They must be equidistant from the line.

(Remember your physics concept on plane mirror images, the distance between object and mirror , and distance between image and mirror are the same)

Next,

Reflection means the circle's size doesn't change, so the radius is unchanged.


Use the centre of C2 that you found and the radius to form the equation for it.

Then sub (9,2) to see if it satisfies the equation
(i.e LHS must equal RHS)


You can type your answers later to verify with me if needed.

thx :) managed to complete this qn too

Great