Perpendicular equation: y = ax+14
Slope of line: 2-6/1-b = -1/a
Multiply both sides by 1-b: -4 = -1+b/a
By trial and improvement: -4 = -1+9/-2
By trial and improvement: -4 = -1-9/2.5
Therefore: a = -2 and b = 9 or a = 2.5 and b = -9
Their values work out as: a = -2 and b = 4
Possible values: a = -2 and b = 9 or a = 5/2 and b = -9 Drawing a sketch on graph paper with the information already given helps.
In its general form of a straight line equation the perpendicular bisector equation works out as:- x-3y+76 = 0
The values of p and q work out as -2 and 4 respectively thus complying with the given conditions.
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
Their values work out as: a = -2 and b = 4
True. (Apex)
Possible values: a = -2 and b = 9 or a = 5/2 and b = -9 Drawing a sketch on graph paper with the information already given helps.
In its general form of a straight line equation the perpendicular bisector equation works out as:- x-3y+76 = 0
The values of p and q work out as -2 and 4 respectively thus complying with the given conditions.
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
They must be equidistant from the point of bisection which is their midpoint and works out that a = -2 and b = 4 Sketching the equations on the Cartesian plane will also help you in determining their values
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
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
The slope of the line is 1/4 So the values are t = -2 and v = 4 Because they satisfy the equation: (v-2)/6-t = 2/8 = 1/4
If the points are (b, 2) and (6, c) then to satisfy the straight line equations it works out that b = -2 and c = 4 which means that the points are (-2, 2) and (6, 4)