Maths(Coordinate Treatment of Simple Locus Problems)

2007-05-18 11:35 pm

1.Find the points of intersection of the line y=2x+1 and the circle x^2+y^2+2x-8y-8=0.

2.A(2,2) is a point on the cicle C:x^2+y^2+2x+4y-20=0.Find the equation of the tangent to C at A.

3.If y=mx is a tangent to the circle x^2+y^2-4x+2y+4=0,find the values of m.

回答 (1)

hang

2007-05-19 1:40 am

✔ 最佳答案

1)
y = 2x + 1 and x^2 + y^2 + 2x - 8y - 8 = 0

x^2 + (2x + 1)^2 + 2x - 8(2x + 1) - 8 = 0

x^2 + 4x^2 + 4x + 1 + 2x - 16x - 8 - 8 = 0

5x^2 - 10x - 15 = 0

x^2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = -1 or x = 3
y = -1 or y = 7

the points are (-1,-1) and (3,7)

2)
the tangent is:

2x + 2y + (2)(2 + x)/2 + (4)(2 + y)/2 - 20 = 0

2x + 2y + 2 + x + 4 + 2y - 20 = 0

3x + 4y - 14 = 0

3)
y = mx

x^2 + y^2 - 4x + 2y + 4 = 0

centre:(2,-1) , radius:1

|(2m + 1) / sqrt(m^2 + 1)| = 1

4m^2 + 4m + 1 = m^2 + 1

3m^2 + 4m = 0

m(3m + 4) = 0

m = 0 or m = -4/3

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