Difficult Maths Problems

Page 1

The Diagram shows the circle x2 + y2 = 10

Point P lies on the circle and has x coordinate 1

The Tangent at P intersects the x-axis at Q

Work out the coordinate of Q

X2 + Y2 = r2

r2 = 10

r = Sqrt 10

l2 + h2 = sqrt 10 2

h2 = 10 - 1

h2 = 9

h =3

M = 3/1 = 3

mpa = -1/3

Y = mx + c

3=-1/3 + c

3x 1/3 = c

10/3 = c

3 = -1/3 x 1 + c

y = -1/3x + 10/3

Page 2

The diagram shows a line joining O to P

The gradient of the line is 2

The length of the line is sqrt2645

Work out the coordinates of P

(2c)2 + c2 = 2sqrt2645

4c2+c2 = 2645

5c2 = 2645

c2 = 2645/5

c2 = 529

c = sqrt529

c = 23

23 x 2 = 46

x = 23

y = 46

Page 3

A (-2,1), B (6,5) and C (4,k) are the vertices of a right-angled triangle ABC. Angle ABC Is a right angled triangle.

Find an equation of the line that passes through A and C

Give your answer in the form ay + bx = c where a, b and c are integers.

Gradient AB = 5-1 = 4 = 1

6--2 8 2

Gradient BC = -2

Y = mx + c passes through B

5 = -2*6 + c

5 + 12 = c

y = -2x + 17

Coordinate C => y =-2 x 4 +17

=> 9

=> (4,9)

Equation of line between A (2,1) and C (4,9)

M => 9-1 = 8

=> 4--2 = 6

y = 4/3 x + c

9 = 4/3 x+ c

27-16 = c

3 3

c = 11/3

y = 4/3x + 11/3

x3

3y - 4x = 11