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How do you find the possible values of n when the straight line y equals nx plus 1 is tangent to the curve 3x squared minus 4x plus 4?
Wiki User
∙ 13y ago
By definition: 3x2-4x+4 = nx+1
Form a quadratic equation: 3x2+(-4x-nx)+3 = 0
For the line to be tangent to the curve the discriminant b2-4ac of the quadratic equation must equal zero.
Hence:
(-4-n)2-4*3*3 = 0
(-4-n)2-36 = 0
(-4-n)2 = 36
Square root both sides:
4+n = +/- 6
n = +/-6 -4
Therefore the values of n are 2 or -10
Wiki User
∙ 13y ago
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What are the possible value of k when the line y equals x plus k is a tangent to the circle x squared plus y squared equals 25?
They are +/- 5*sqrt(2)
What is the value of k when the straight y equals 3x-1 is a tangent to the curve x squared plus y squared equals k?
2
What is the value of k when y equals 3x plus 1 and is a line tangent to the curve of x squared plus y squared equals k?
k = 0.1
How do you solve secant squared divided by tangent?
In trig, the secant squared divided by the tangent equals the hypotenuse squared divided by the product of the opposite and adjacent sides of the triangle.Details: secant = hypotenuse/adjacent (H/A) and tangent = opposite/adjacent (A/O);Then secant2/tangent = (H2/A2)/(O/A) = H2/A2 x A/O = H2/AO.
How can you prove that the straight line of y equals x plus k is a tangent to the curve of x squared plus y squared equals 4 and only when k squared equals 8?
You don't.Furthermore, how would you prove your not a virgin? Either way your fu'd.Improved Answer:-y = x+kx2+y2 = 4Substitute y = x+k into the bottom equation:x2+(x+k)(x+k) = 4x2+x2+2kx+k2 = 4k2 = 8 so therefore:2x2+2kx+8-4 = 0 => 2x2+2kx+4 = 0For the straight line to be a tangent to the curve the discriminant b2-4ac of the quadratic equation must equal zero:Hence:-(2*k)2-4*2*4 = 0k2 = 8So: 4*8-4*2*4 = 0 => 32-32 = 0Therefore the straight line y = x+k is a tangent to the curve x2+y2 = 4
What are the possible value of k when the line y equals x plus k is a tangent to the circle x squared plus y squared equals 25?
They are +/- 5*sqrt(2)
What is the value of k when the straight y equals 3x-1 is a tangent to the curve x squared plus y squared equals k?
2
At what point is the line of y equals x -4 tangent to the curve of x squared plus y squared equals 8?
(2, -2)
What is the value of k when y equals 3x plus 1 and is a line tangent to the curve of x squared plus y squared equals k?
k = 0.1
How do you solve secant squared divided by tangent?
In trig, the secant squared divided by the tangent equals the hypotenuse squared divided by the product of the opposite and adjacent sides of the triangle.Details: secant = hypotenuse/adjacent (H/A) and tangent = opposite/adjacent (A/O);Then secant2/tangent = (H2/A2)/(O/A) = H2/A2 x A/O = H2/AO.
Find the equations of the lines that are tangent to the ellipse x squared plus y squared equals sixteen and that also pass through the point x equals 4 and y equals 6?
This is not possible, since the point (4,6) lies inside the circle : X2 + Y2 = 16 Tangents to a circle or ellipse never pass through the circle
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)
How can you prove that the straight line of y equals x plus k is a tangent to the curve of x squared plus y squared equals 4 and only when k squared equals 8?
You don't.Furthermore, how would you prove your not a virgin? Either way your fu'd.Improved Answer:-y = x+kx2+y2 = 4Substitute y = x+k into the bottom equation:x2+(x+k)(x+k) = 4x2+x2+2kx+k2 = 4k2 = 8 so therefore:2x2+2kx+8-4 = 0 => 2x2+2kx+4 = 0For the straight line to be a tangent to the curve the discriminant b2-4ac of the quadratic equation must equal zero:Hence:-(2*k)2-4*2*4 = 0k2 = 8So: 4*8-4*2*4 = 0 => 32-32 = 0Therefore the straight line y = x+k is a tangent to the curve x2+y2 = 4
What is the value of y when y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x then it works out that when x = 5/8 then y = 5/2
What is cotangent 32 equals tangent x?
Cotangent 32 equals tangent 0.031
Would the graph of y equals x squared be a straight line on log paper?
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How do you prove that the straight line y equals x plus c is a tangent to the curve x squared plus y squared equals 4 when c squared equals 8?
The general form of a line tangent to a circle is:y=mx+a(1+m2 )1/2. where "a" is the radius of the circle. Here circle is x2 + y2=4, so radius=a=2. nowc2=a2(1+m2)=8 (given)or 8=4(1+m2)2=1+m2 orm2=1 orm=1. so equation becomesy=mx+c ory=x+cImproved Answer:Equation 1: y = x+square root of 8 => y2 = x2+square root of 32x+8 when both sides are squared.Equation 2: y2 = 4-x2By definition:x2+the square root of 32x+8 = 4-x2 => 2x2+the square root of 32x+4 = 0If the discriminant b2-4ac of the above quadratic equation is equal to zero then this is proof that the straight line is tangent to the curve:b2-4ac = the square root of 322-4*2*4 = 0Therefore the straight line is a tangent to the curve because the discriminant of the quadratic equation equals zero.
