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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?
Wiki User
∙ 6y ago
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
Wiki User
∙ 6y ago
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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
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 shape can not form a perpendicular bisector?
A circle cannot form a perpendicular bisector.
Which of these can not form a perpendicular bisector?
Perpendicular bisector lines intersect at right angles
Does the perpendicular bisector of a cord of a circle passe through the center of the circle?
Yes, the perpendicular bisector of a cord is the shortest distance from the centre of a circle to the cord.
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
Which of these tools or constructions is used to inscribe a square inside a circle?
Perpendicular bisector.
How do you find center of a circle given 3 points on the circle?
You have points A, B, and C. Using a compass and straight edge, find a perpendicular bisector of AB (that is, a line that is perpendicular to AB and intersects AB at the midpoint of AB. Next, find a perpendicular bisector of BC. The two lines you found will meet at the center of the circle.
What is a method for constructing a regular quadrilateral?
Start with constructing a circle, then make a diameter from that circle. After you've done that, construct the perpendicular bisector of, the diameter, then draw the line in from the perpendicular bisector. After you've done that, connect the 4 points you have on the circle... then you're done. ^^ Hope this helps. :)
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
What is the perpendicular bisector equation of the chord y equals x plus 5 within the circle x2 plus 4x -18y plus 59 equals 0?
x² + 4x - 18y + 59 = 0 is not a circle; it can be rearranged into: y = (x² + 4x + 59)/18 which is a parabola. You have missed out a y² term. ------------------------------------------------------------ Assuming you meant: x² + 4x + y² - 18y + 59 = 0, then: The perpendicular bisector of a chord passes through the centre of the circle. The slope m' of a line perpendicular to another line with slope m is given by m' = -1/m The chord y = x + 5 has slope m = 1 → the perpendicular bisector has slope m' = -1/1 = -1 A circle with centre Xc, Yc and radius r has an equation in the form: (x - Xc)² + (y - Yc)² = r² The equation given for the circle can be rearrange into this form by completing the square in x and y: x² + 4x + y² - 18y + 59 = 0 → (x + (4/2))² - (4/2)² + (y - (18/2))² - (18/2)² + 59 = 0 → (x + 2)² +(y - 9)² - 2² - 9² + 59 = 0 → (x + 2)² + (y - 9)² = 4 + 81 - 59 → the circle has centre (-2, 9) (The radius, if wanted, is given by r² = 4 + 81 - 59 = 36 = 6²) The equation of a line with slope m' through a point (Xc, Yc) has equation: y - Yc = m'(x - Xc) → y - 9 = -1(x - -2) → y - 9 = -x - 2 → y + x = 7 The perpendicular bisector of the chord y = x + 5 within the circle x² + 4x + y² - 18y + 59 = 0 is y + x = 7
