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Several Math Problems (Equation about Circle)
1, circle c: x 2+y 2-6x-8y+24 = 0. If the circle symmetric about the straight line x-y- 1=0 is C', then the equation of the circle C' is

Circle c: x 2+y 2-6x-8y+24 = 0 The circle that is symmetrical about the straight line x-y- 1=0 is C', and the equation of the circle C' is

The equation of the line connecting the two centers is set to X+Y+C=0,

Substituting into the center (3, 4) of circle C, X+y-7=0,

Simultaneous X-Y- 1=0, X+Y-7=0, (4,3),

Let another circle (x, x-7), x+3/2=4, x-7+4/2=3,

(5,9), the equation of another circle is (X-5)∧2+(Y-9)∧2= 1.

2. The chord length of a circle x 2+y 2-4x+4y+6 = 0 equals _ _ _

x^2+y^2-4x+4y+6=0

(x^2-4x+4)+(y^2+4y+4)=2

(x-2)^2+(y+2)^2=2

Center (2, -2), radius √2

Distance from center of circle to straight line

|2+2-5|/√( 1+ 1)= 1/√2

Half the chord length 2+( 1/√ 2) 2 = (√ 2) 2

Half chord length 2+ 1/2 = 2.

Half the chord length =√(3/2)=√6/2.

Chord length =√6

(3) If the line mx+ny= 1 intersects the circle X 2+Y 2 = 1, then the point (m, n) is in the circle _ _ _

x=m,y=n

M 2+n 2 = 1, then (m, n) is a point on the circle!