As there is no change in y, the perpendicular bisector is given by x = (10 + k)/2
This is given as x = 7; thus:
→ (10 + k)/2 = 7
→ 10 + k = 14
→ k = 4
In its general form of a straight line equation the perpendicular bisector equation works out as:- x-3y+76 = 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
the answer on A+ is 2.5 cm
If: y = 5x +10 and y = x^2 +4 Then: x^2 +4 = 5x +10 Transposing terms: x^2 -5x -6 = 0 Factorizing the above: (x-6)(X+1) = 0 meaning x = 6 or x = -1 Therefore by substitution endpoints of the line are at: (6, 40) and (-1, 5) Midpoint of line: (2.5, 22.5) Slope of line: 5 Perpendicular slope: -1/5 Perpendicular bisector equation: y-22.5 = -1/5(x-2.25) => 5y = -x+114.75 Perpendicular bisector equation in its general form: x+5y-114.75 = 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
14
True. (Apex)
In its general form of a straight line equation the perpendicular bisector equation works out as:- x-3y+76 = 0
2.50 cm
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
the answer on A+ is 2.5 cm
If: y = 5x +10 and y = x^2 +4 Then: x^2 +4 = 5x +10 Transposing terms: x^2 -5x -6 = 0 Factorizing the above: (x-6)(X+1) = 0 meaning x = 6 or x = -1 Therefore by substitution endpoints of the line are at: (6, 40) and (-1, 5) Midpoint of line: (2.5, 22.5) Slope of line: 5 Perpendicular slope: -1/5 Perpendicular bisector equation: y-22.5 = -1/5(x-2.25) => 5y = -x+114.75 Perpendicular bisector equation in its general form: x+5y-114.75 = 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
Points: (1, 2) and (9, 6) Midpoint: (5, 4) Slope: 1/2 Perpendicular slope: -2 Perpendicular bisector equation: y-4 = -2(x-5) => y = -2x+14 Therefore: k = -2 thus satisfying the given bisector equation
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
Their values work out as: a = -2 and b = 4
Equation of circle: x^2 +4x +y^2 -18y +59 = 0 Completing the squares: (x+2)^2 +(y-9)^2 = 26 Equation of chord: y = x+5 Endpoints of chord: (-1, 4) and (3, 8) Midpoint of chord: (1, 6) Center of circle: (-2, 9) Slope of chord: 1 Slope of radius: -1 Perpendicular bisector equation of chord: y-6 = -1(x-1) => y =-x+7