Given pair of lines are x² + 4xy + y² = 0
⇒ (y/x) ² + 4 y/x + 1 = 0
⇒ y/x = -4±2√3/2 = -2±√3,
∴ The lines y = (-2 + √3) x and y = (-2 - √3) x and x - y = 4 forms an equilateral triangle
Clearly the pair of lines x² + 4xy +y² = 0 intersect at origin,
The perpendicular distance form origin to x - y = 4 is the height of the
h = 2 √ 2
∵ Area of triangle = h²/√3 = 8/√3
Yes you use the method of your choice to solve (x+7)*(x+7)
Then you distribute the negative -1(x^2+14x+49)
Then you add the four
-x^2-14x-45 should be your answer
Since -5 and -5 are the same number, they are on the same y axis so the only distance we need to calculate is between the X coordinates.
When looking for distance, you can not have a negative. what |-3|+|9| is looking for is the distance from 0 on the X axis. since distance can't be negative, (you go 3 miles away from your house in one direction, vs 3 miles in the opposite. both ways is positive, even with opposite directions. same with axis, it doesnt matter which way, only the number.) you need the absolute value of -3 to get the distance from the 0 on the x axis.
short version: distance is positive, and its adding the distances from the x axis to get distance from each other
The answer for what the ratio is for 4% is 4:100
