Solution: Drawing: A square (2) with known intercept of X axis and Y axis as plus or minus 1 and side length as root sign.
So the area is 2.
The chord length of the straight line X-Y+4=0 cut by the circle (X+2) square +(Y-2) square =2 is
Solution: Use the combination of numbers and shapes, (just draw a circle and a straight line)
The distance from the center of the circle (-2,2) to the straight line is d= 0, so the chord length is the diameter: the root sign (2).
3 If point A (-4,0) is tangent to the square of circle (X+7)+the square of circle (y +(Y+8) =9, the tangent equation is
Solution: (If you know the slope of a straight line, you can find the equation of the straight line) Let the slope of the tangent be k, then
The tangent equation is y= k (x+4), that is, kx-y+4k = 0-( 1).
The distance from the center of the circle to the tangent is the radius, so the formula of the distance from the point to the straight line is: k=- 55/48.
Substitute it into the formula (1), and you can do it.
4 The equation of a circle with the center at (1, 1) and tangent to the straight line 3x+4y+3=0 is
Solution: The center of the circle is already known, just find the radius.
The circle is tangent to the straight line, so the radius is the distance from the center of the circle to the straight line.
So the radius =2 (using the distance formula from point to straight line)
So the equation of the circle is: (X- 1) 2+(Y- 1) 2 = 4.