a Show that x 2 y 2 10x 8y 32 0 can be written in the form (x a) 2 (y b) 2 r 2 , where a, b and r are numbers to be found b Circle C has equation x 2 y 2 10x 8y 32 0 and circle D has equation x 2 y 2 9 Calculate the distance between the centre of circle C and the centre of circle D c Using your ans...

a To write the equation in the form x a2 y b2 r2 we need to complete the square for both x and y terms Given equation x2 y2 10x 8y 32 0 Rearranging te ...

a. Show that x 2 + y 2 10x 8y + 32 = 0 can

Question:

a. Show that x² + y² − 10x − 8y + 32 = 0 can be written in the form (x − a)² + (y − b)² = r², where a, b and r are numbers to be found.

b. Circle C has equation x² + y² − 10x − 8y + 32 = 0 and circle D has equation x² + y² = 9. Calculate the distance between the centre of circle C and the centre of circle D.

c. Using your answer to part b, or otherwise, prove that circles C and D do not touch.

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