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)
14
False. 1). The proposed equation y=mx suggests that the chord's right bisector has no y-intercept, i.e. passes through the origin. This is interesting, and appears plausible, and I'm willing to acknowledge that this aspect of it is true. But ... 2). If the slope of the chord is 'm', then the slope of its right bisector is not also 'm'. If it were, that would make the chord and its bisector parallel, which would be pretty silly. The slope of any line perpendicular to the chord, including its right bisector, has to be '-1/m'. The equation of the chord's right bisector is: Y = -X/m .
The equation will be perpendicular to the given equation and have a slope of 3/4:- Perpendicular equation: y--3 = 3/4(x--2) => 4y--12 = 3x--6 => 4y = 3x-6 Perpendicular equation in its general form: 3x-4y-6 = 0
Known equation: y = 2x+10 Perpendicular equation: 2y = -x+10 Both equations intersect at: (-2, 6) Distance from (2, 4) to (-2, 6) is sq rt of 20 using the distance formula
2.50 cm
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
Their values work out as: a = -2 and b = 4
True. (Apex)
In its general form of a straight line equation the perpendicular bisector equation works out as:- x-3y+76 = 0
The x and y axes on the Cartesian plane are perpendicular to each other at the point of origin
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
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
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.
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