I WILL GIVE BRAINLY
1 answer:
9514 1404 393
Answer:
m^2 = 35/9
Step-by-step explanation:
The line will be tangent to the ellipse where there is one point of intersection between the line and the ellipse. We can find that case by looking at the discriminant of the quadratic.
x^2 +9(mx +2)^2 = 1
x^2 +9(m^2x^2 +4mx +4) = 1
(9m^2 +1)x^2+36mx +35 = 0 . . . . subtract 1, collect terms
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Then the discriminant is ...
(36m)^2 -4(9m^2 +1)(35)
We want it to be zero, so we have ...
1296m^2 -1260m^2 -140 = 0 . . . . eliminate parentheses
36m^2 = 140 . . . . . . . . . . . . . . . add 140
m^2 = 140/36 . . . . . . . . . . . . divide by 36
m^2 = 35/9
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y=kx and y= are two equations of constant of proportionality
Step-by-step explanation:
There are two equations for the constant of proportionality. That is
(i) Direct proportion
(ii) Inverse proportion
In direct proportion y=kx, Now
if x increases, then y also increases and if x decreases, then y also decreases. So, k is a constant proportionality.
In Inverse proportion y=, Now
if x increases then y decreases and if x decreases, then y increases and k is a constant proportionality.
In direct proportion, we put y=1 and x=2, So k=.
So, the equations y=kx and y= are two equations of constant of proportionality.