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!