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Where are the two points of contact when the line 2x plus 5y equals 4 crosses the curve y squared equals x plus 4 on the Cartesian plane?
Wiki User
∙ 7y ago
There are two simultaneous equations to solve:
- 2x + 5y = 4
- y² = x + 4
The second can be rearranged to make x the subject, substituted into the first and the values of y found:
y² = x + 4 → x = y² - 4
2x + 5y = 4
→ 2(y² -4) + 5y = 4
→ 2y² -8 + 5y - 4 = 0
→ 2y² +5y - 12 = 0
→ (2y - 3)(y + 4) = 0
→ y = 1½ or -4
These values can be substituted into either equation to find the value of x; I'll use the second:
y² = x + 4
→ x = y² - 4
- y = 1½ → x = (3/2)² - 4 = 9/4 - 16/4 = -7/4 = -1¾
- y = -4 → x = (-4)² - 4 = 16 - 4 = 12
Wiki User
∙ 7y ago
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Where are the points of contact when the line 2x plus 5 equals 4 crosses the curve y squared equals x plus 4 on the Cartesian plane?
The two solutions are (x, y) = (-0.5, -sqrt(3.5)) and (-0.5, sqrt(3.5))
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What number squared equals 30?
5.477225575 squared equals 30.
Where are the points of contact when the line 2x plus 5 equals 4 crosses the curve y squared equals x plus 4 on the Cartesian plane?
The two solutions are (x, y) = (-0.5, -sqrt(3.5)) and (-0.5, sqrt(3.5))
What is x squared plus 25 times y squared equals 50?
It is the Cartesian equation of an ellipse.
What are the points of intersection of 3x -2y -1 equals 0 with 3x squared -2y squared equals -5 on the Cartesian plane?
Points of intersection work out as: (3, 4) and (-1, -2)
What are the points of contact that the curve of y equals x squared -x -12 makes with the x and y axes on the Cartesian plane?
If: y = x2-x-12 Then points of contact are at: (0, -12), (4, 0) and (-3, 0)
What is the value of k when y equals 3x plus 1 is a line tangent to the curve of x squared plus y squared equals k hence finding the point of contact of the line to the curve?
It is (-0.3, 0.1)
What is the relationship between the line y equals x plus 4 and the circle x squared plus y squared -8x plus 4y equals 30 on the Cartesian plane explaining how and why?
Equations: y = x+4 and x^2 +y^2 -8x +4y = 30 The given equations will finally form a quadratic equation such as: x^2 +2x +1 = 0 Discriminant: 2^2 -4*(1*1) = 0 meaning there are equal roots Because the discriminant has equal roots the line is a tangent to the circle In fact the line makes contact with the circle at (-1, 3) on the Cartesian plane
What number squared equals 30?
5.477225575 squared equals 30.
What equals 121 when its squared?
The number that equals 121 when squared is 11.
Where is the vertex coordinate of the parabola y equals 24 -6x -3x squared when plotted on the Cartesian plane?
The vertex coordinate point of the vertex of the parabola y = 24-6x-3x^2 when plotted on the Cartesian plane is at (-1, 27) which can also be found by completing the square.
What is a squared plus b squared equals c squared when a equals 2 and c equals 6?
b = sqrt32 or 4 root 2
Does 6xy-8xy equals -2x squared y squared?
No, it equals -2xy. lrn2math
Where are the points of contact when the line 3x -y equals 5 passes through the curve 2x squared plus y squared equals 129?
It works out that line 3x-y = 5 makes contact with the curve 2x^2 +y^2 = 129 at (52/11, 101/11) and (-2, -11)
