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What are the points of intersection of the line x -2 equals 2 with x2 -4y2 equals 5?
Wiki User
∙ 6y ago
x - 2 = 2
→ x = 4
→ x² - 4y² = 5
→ 4² - 4y² = 5
→ 4y² = 16 - 5
→ 4y² = 11
→ y² = 11/4
→ y = ± √(11/4)
→ The points of intersection of x - 2 = 2 with x² - 4y² = 5 are (4, -√(11/4)) ≈ 4, -1.658) and (4, √(11/4)) ≈ 4, 1.658)
Wiki User
∙ 6y ago
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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)
Does 2y squared equals 4y?
No, it equals 4y2
What is y in x equals 4y2 plus 6 when x equals 42?
In the equation x = 4y2 + 6 where x = 42, we need to substitute 42 for x and solve for y. x = 4y2 + 6 42 = 4y2 + 6 42 - 6 = 4y2 + 6 - 6 36 = 4y2 36 / 2 = 4y2 / 2 18 = 4y 18 / 4 = 4y / 4 9 / 2 = y 4 1/2 = y (or 4.5 = y)
4y 2nd power equals 3- 5?
4y2
What are the points of intersection of the equations of 3x minus 2y equals 1 and 3x squared minus 2y squared plus 5 equals 0 showing details of your work?
A: 3x-2y = 1 => 3x = 1+2y B: 3x2-2y2+5 = 0 => 3x2 = 2y2-5 Square both sides in equation A: 9x2 = 1+4y+4y2 Multiply all terms by 3 in equation B: 9x2 = 6y2-15 So it follows that:- 6y2-15 = 1+4y+4y2 and 6y2-15-1-4y-4y2 = 0 Collect like terms: 2y2-4y-16 = 0 Divide all terms by 2: y2-2y-8 = 0 Factorise: (y-4)(y+2) = 0 Therefore: y = 4 or y = -2 Substitute the above y values into the linear equation to find the values of x: The points of intersection are: (3, 4) and (-1,-2)
What are the points of intersection of 3x -2y equals 1 with 3x squared -2y squared plus 5 equals 0?
3x - 2y = 1 => 3x = 2y + 1 => x = (2y + 1)/3 Substitute this value in the other equation: 3*[(2y + 1)/3]2 - 2y2 + 5 = 0 3*[4y2/9 + 4y/9 + 1/9] - 2y2 + 5 = 0 4y2/3 + 4y/3 + 1/3 - 2y2 + 5 = 0 Multiplying through by 3, gives 4y2 + 4y + 1 - 6y2 + 15 = 0 2y2 - 4y - 16 = 0 y2 - 2y - 8 = 0 (y - 4)*(y + 2) = 0 So y = 4 or y = -2 when y = 4, x = (2*4 + 1)/3 = 9/3 = 3 and when y = -2, x = (2*-2 + 1)/3 = -1 So the points of intersection are (3, 4) and (-1, -2)
What are the points of intersection when the line x -2y equals 1 crosses the curve 4y2 -3x2 equals 1?
If: x -2y = 1 then x = 1 +2y If: 4y^2 -3x^2 = 1 then 4y^2 -3(1 +2y)^2 -1 = 0 Removing brackets: 4y^2 -3 -12y -12y^2 -1 = 0 Collecting like terms: -8y^2 -4 -12y = 0 Dividing all terms by -4: 2y^2 +1 +3y = 0 Factorizing the above: (2y+1)(y+1) = 0 meaning y = -1/2 or y = -1 Therefore points of intersection by substitution are at: (0, -1/2) and (-1, -1)
What are the coordinates of the line x-y equals 2 that intersects the of curve x squared-4y squared equals 5?
If you mean the coordinates of the line x-y = 2 that intersects the curve of x2-4y2 = 5 Then the coordinates work out as: (3, 1) and (7/3, 1/3)
How do you find the solution to x2-4y2 equals 16 and 2y-x equals 2?
x2 - 4y2 = 16∴ (x - 2y)(x + 2y) = 162y - x = 2∴ x = 2y - 2∴ ([2y - 2] - 2y)([2y - 2] + 2y) = 16∴ (y - 1 - y)(y - 1 + y) = 16∴ -1(2y - 1) = 16∴ 1 - 2y = 16∴ -2y = 15∴ y = -7.52y - x = -2∴ -15 - x = -2∴ x = -13So the point of intersection is (-13, -7.5)
What conic section does the equation x2 4y2 6x 8y plus 1 equals 0 represent?
hyperbola
How do you do the special factorization of cubes for 27 plus 64y6?
(4y2 + 3)(4y2 - 6y + 3)(4y2 + 6y + 3)
How do you solve 4y2 37a-150?
4y2+37a-15=0
