Equation of a Circle Answers AWS

Equation of a Circle Answers GCSE Mathematics HA16 1.

Write the equation of the circle with a centre at (0, 0) and a radius of 6.

Answer:

2.

x2 + y2 = 62 x2 + y2 = 36

A circle with its centre at (0, 0) has equation x2 + y2 = 81. Find the length of its diameter.

Answer:

3.

x2 + y2 = r2

x2 + y2 = r2 x2 + y2 = 81

r2 = 81 r = 81 = 9

d = 2r = 2 x 9 = 18

The diagram shows a circle with centre O and the point (8, 15) which lies on the circle. Write the equation of this circle. y

(8,15)

Answer:

O x

4.

x2 + y2 = r2 82 + 152 = r2 64 + 225 = r2 289 = r 17 = r

x2 + y2 = 289

Find the coordinates of the point A knowing that the circle has its centre at (0, 0) and that the point (5, 12) lies on the circle. y

(5,12)

Answer:

A x







x2 + y2 = r2 8 + 122 = r2 25 + 144 = r2 169 = r2 169 = r 13 = r 2

A (13, 0)

Equation of a Circle Answers GCSE Mathematics HA16 5.

Find the equation of the tangent to x2 + y2 = 100 at the point (8, 6).

Answer:

Gradient of radius = 6 = 3 8 4 Gradient of tangent = -1 = gradient of radius = y = mx + c m = -4 x=8 y=6 3 6 = -4 (8) + c 3

6 = -32 + c 3

-1 /4 -4 3

3

6 + 32 = c 3

50 = C 3

y = -4x + 50 3 3 y = -4x + 50 3

6.

or

3y = - 4x + 50

The line y = -2x + 10 is a tangent to the circle x2 + y2 =20 at the point P. Find the coordinates of point P.

Answer:

substitute y = -2x + 10 into x2 + y2 = 20 x2 + (-2x + 10)2 = 20



x2 + 4x2 - 40x + 100 = 20



5x2 - 40x + 80 = 0



x2 - 8x + 16 = 0 (x - 4) (x - 4) = 0



x-4=0

If x = 4 then y = -2 (4) + 10 = 2 * P (4,2)

so

x=4

5