Find the angle between the curves given below X2+3y=3,x2-y2 +25=0
Answers
Given : curves
x² + 3y = 3
x² - y² + 25 = 0
To Find : angle between the curves
Solution:
x² + 3y = 3
x² - y² + 25 = 0 => x² = y² - 25
y² - 25 + 3y = 3
=> y² + 3y - 28 = 0
=> y² + 7y - 4y - 28 = 0
=> (y + 7)(y - 4) = 0
=> y = -7 , 4
x² = y² - 25 => x² = 24 or - 9
- 9 not possible
Hence x² = 24
=> x = ±2√6
Points of intersection ±2√6 , -7
Taking point
2√6 , -7
x² + 3y = 3 => dy/dx = -2x/3 = -4√6/3
x² - y² + 25 = 0 => dy/dx = x/y = -2√6 /7
Angle between line = α
tan α = | (-4√6/3 - (-2√6 /7))/(1 + (-4√6/3)( -2√6 /7)|
=> tan α =| (-28√6 +6√6) (21 + 48) |
=> tan α = | (-22√6) /69 |
=> tan α = | (-22√6) /69 |
α = 37.99°
angle between curves = 38° or 152°
Learn More:
Derive an expression for acute angle between two lines slopes m1 ...
brainly.in/question/12863695
Using your protractor, draw an angle of measure 108°. With this ...
brainly.in/question/15910817
find the equation of the bisector of the obtuse angle between the ...
brainly.in/question/11991231
