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secondary 3 | A Maths

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'Find the radius and centre'

Ok ive been staring at this qn for 2 days i still cant figure it out

y-coordinate of B is definitely 5.

We form one “normal to curve” equation at that tangent and then solve with y = 5 to find the x-coordinate of centre.

Radius is easy after thatz

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Let coordinates of centre be (a,b)

Now radius is always the same from any point on the circle's circumference to the centre.

So length from each point to the centre is the same.

Use formula Length = √[(x2 - x1)² + (y2 - y1)²]

√[(0 - a)²+(5 + 2√21 - b)²] = √[(0 - a)²+(5 - 2√21 - b)²]

We can square both sides. Expression becomes

a² + (5 + 2√21 - b)² = a² + (5 - 2√21 - b)²

(5 + 2√21)² - 2b(5 + 2√21) + b² = (5 - 2√21)² - 2b(5 - 2√21) + b²

5² + 20√21 + 84 - 10b - 4b√21 = 5² - 20√21 + 84 - 10b + 4b√21

8b√21 = 40√21

b = 5

So the y coordinate is 5.