Answer:
see explanation
Step-by-step explanation:
The 2 angles form a right angle, thus their sum is 90°, hence
4x + 7 + 35 = 90
4x + 42 = 90 ( subtract 42 from both sides )
4x = 48 ( divide both sides by 4 )
x = 12
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To calculate the slope m use the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line
m = =
= 4
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
