有a.maths 唔識做

1)
The circle: x2 + y2 = 4 ...... (1)

The line: x + y = 1
Slope of the line = -1

The tangent ^ the above line.
Hence, the slope of the tangent = 1
Equation of the tangent : y = x + C ...... (2)

The tangent touches the circle.
Put (2) into (1)
x2 + (x + C)2 = 4
x2 + x2 + 2Cx + C2 = 4
2x2 + 2Cx + (C2 - 4) = 0

∆ = 0
(2C)2 - 4(2)(C2 - 4) = 0
4C2 - 8C2 + 32 = 0
-4C2 + 32 = 0
C2 - 8 = 0
C2 = 8
C = 2√2 ooro C = -2√2

When C = 2√2,
Equation of the tangent: y = x + 2√2
Equation of the tangent: x - y + 2√2 = 0

When C = -2√2
Equation of the tangent: y = x - 2√2
Equation of the tangent: x - y - 2√2 = 0

Equations of the tangents are: x - y + 2√2 = 0
Equations of the tangents are: x - y - 2√2 = 0
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