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How do you find the points of intersection of the curve and straight line of y equals 8 over x and y equals 7 plus x?
Wiki User
∙ 13y ago
y = 8/x and y = 7+x
So by definition:
7+x = 8/x
Multiply all terms by x:
7x+x2 = 8
Subtract 8 from both sides and form a quadratic equation:
x2+7x-8 = 0
Factor the equation:
(x-1)(x+8) = 0
So x = 1 or x = -8
Substitute the above values into the original equations to find the values of y:
Therefore the points of intersection are (-8,-1) and (1, 8)
Wiki User
∙ 13y ago
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What are the points of intersection of the line y equals -8-3x with the curve y equals -2-4x-x squared?
They work out as: (-3, 1) and (2, -14)
What are the points of intersection between the line x -y equals 2 and the curve x2 -4y2 equals 5?
Equations: x -y = 2 and x^2 -4y^2 = 5 By combining the equations into a single quadratic equation in terms of y and solving it: y = 1/3 or y = 1 By means of substitution the points of intersection are at: (7/3, 1/3) and (3, 1)
Which is a secant?
Secant is a straight line that intersects a curve at two or more points
What are the points of intersection of the line of x -2y equals 1 with the curve of 3xy -y squared equals 8 showing work?
If: x-2y = 1 and 3xy-y2 = 8 Then: x =1+2y and so 3(1+2y)y-y2 = 8 => 3y+5y2-8 = 0 Solving the quadratic equation: y = 1 or y = -8/5 Points of intersection by substitution: (3, 1) and (-11/5, -8/5)
How do you find the points of intersection of the straight line x -2y equals 1 with the curve 3xy - y squared equals 8?
x-2y = 1 => x = 2y+1 3xy-y2 = 8 Substitute x = 2y+1 into the second equation: 3y(2y+1)-y2 = 8 6y2+3y-y2 = 8 5y2+3y-8 = 0 Solving the above with the quadratic equation formula will give y values of: -8/5 and 1 Substitute these values into the first equation to find the values of x: So the points of intersection are: (3, 1) and (-11/5, -8/5)
What are points of intersection of the line 3x -y equals 5 with the curve of 2x squared plus y squared equals 129?
Straight line: 3x-y = 5 Curved parabola: 2x^2 +y^2 = 129 Points of intersection works out as: (52/11, 101/11) and (-2, -11)
What are the points of intersection of the line y equals -8-3x with the curve y equals -2-4x-x squared?
They work out as: (-3, 1) and (2, -14)
What is a straight curve with no end points?
A circle.
What is a straight line that intersects a curve?
A straight line that intersects a circle or curve at two points, but which has both end points outside the circle or curve is called a secant. A straight line that links two points on a circle or curve is called a chord. A straight line which touches a circle or curve at one point is called a tangent. A straight line that cuts a circle or curve at one point is a straight line.* For moving diagrams see Related links below this box.
A straight curve with no end points?
You had us baffled at "straight curve" . Could you mean if you start at the north pole, walk in a straight line, you will eventually get back to the north pole and round in a circle. Hence a straight line but no end points.
Where are the points of intersection of the straight line 3x -y equals 5 with the curve 2x squared plus y squared equals 129?
(52/11, 101/11) and (-2, -11) Rearrange 3x-y = 5 into y = 3x-5 and substitute this into the curve equation and then use the quadratic equation formula to find the values of x which leads to finding the values of y by substituting the values of x into y = 3x-5.
What are the points of intersection of the straight line x -2y equals 8 with the curve of xy equals 24?
We solved the first equation for 'x': [ x = 2y + 8 ].Then we substituted it for 'x' in the second equation and rearranged: [ y2 + 4y - 12 = 0 ].Solutions of this quadratic equation are: y = 2 and -6. From which x = 12 and -4 .So the straight line intersects the hyperbola at (-4, -6) and at (12, 2) .
What are the points of intersection between the line x -y equals 2 and the curve x2 -4y2 equals 5?
Equations: x -y = 2 and x^2 -4y^2 = 5 By combining the equations into a single quadratic equation in terms of y and solving it: y = 1/3 or y = 1 By means of substitution the points of intersection are at: (7/3, 1/3) and (3, 1)
What is a curve?
A geometrical curve is defined as any set of points. Therefore, counter-intuitively, a straight line is also a geometrical curve.
Whatdoes the word chord mean in math?
It is a straight line joining two different points on a curve which does not cross the curve between those two points.
Which is a secant?
Secant is a straight line that intersects a curve at two or more points
Where are solutions to a system seen on the graph?
The intersection of the individual graphs. In the simplest case, the graph for each equation consists of a line (or some curve); the intersection is the points where the lines or curves meet.
