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What is the perpendicular bisector equation of the line y equals x plus 5 spanning the circle x2 plus 4x plus y2 -18y plus 59 equals 0?
Equation of line: y = x+5
Equation of circle: x^2 +4x +y^2 -18y +59 = 0
The line intersects the circle at: (-1, 4) and (3, 8)
Midpoint of line (1, 6)
Slope of line: 1
Perpendicular slope: -1
Perpendicular bisector equation: y-6 = -1(x-1) => y = -x+7
Perpendicular bisector equation in its general form: x+y-7 = 0
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Is a circle have perpendicular bisector?
A circle can have perpendicular bisector lines by means of its diameter.
What can not form a perpendicular bisector?
A circle cannot form a perpendicular bisector.
What is the perpendicular bisector equation of the chord y equals x plus 5 within the circle x2 plus 4x plus y2 -18y plus 59 equals 0?
Form a simultaneous equation with chord and circle and by solving it:- Chord makes contact with circle at: (-1, 4) and (3, 8) Midpoint of chord: (1, 6) Slope of chord: 1 Slope of perpendicular bisector: -1 Perpendicular bisector equation: y-6 = -(x-1) => y = -x+7
What is the perpendicular bisector equation of the chord y equals x plus 5 within the circle x squared plus 4x plus y squared -18y plus 59 equals 0 showing work?
Chord equation: y = x+5 Circle equation: x^2 +4x +y^2 -18y +59 = 0 Chord end points: (-1, 4) and (3, 8) Chord midpoint: (1, 6) Perpendicular slope: -1 Perpendicular bisector equation: y-6 = -1(x-1) => y = -x+7
What is the perpendicular bisector equation of the chord y equals x plus 5 within the circle x2 plus 4x plus y2 minus 18y plus 59 equals 0?
Chord equation: y = x+5 Circle equation: x^2 +4x +y^2 -18y +59 = 0 Both equations intersect at: (-1, 4) and (3, 8) which are the endpoints of the chord Midpoint of the chord: (1, 6) Slope of chord: 1 Perpendicular slope: -1 Perpendicular bisector equation: y-6 = -(x-1) => y = -x+7
