In geometry, a rectangle is some rectangle with 4 right angles. The word "oblong" is infrequently used to submit on a non-square rectangle. A rectangle with vertices WXYZ would be denoted as WXYZ. All angles are matching. Its middle is equidistant from its vertices, hence it has a circumcircle. Its axis of balance divide opposite sides.
Rectangular equation
Rectangular equation is r^2 = x^2 + y^2
If a rectangle have a length l and width w
Area of the rectangles = A = l * w,
Perimeter of the rectangles = r P = 2l + 2w = 2(l + w),
Every sloping has length 'sqrt{l^2 + w^2},' and after l = w, the rectangle is a square.
Rectangular Equation -examples:
Rectangular equation Example 1:
Change r = 4 to rectangular form.
Given that
r = 4
r^2 = x^2 + y^2, take square two sides we get r^2.
r^2 = 16
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Substitute to rectangular form
x^2 + y^2 = 16
x^2 + y^2 = 16 is the equivalent polar equation to r = 4
Rectangular equation Example 2:
Convert r = 5 cos beta to rectangular form.
Solution:
Since cos = 'x/r' , substitute for cos .
r= 5 * 'x/r'
Multiply two sides by r.
r^2 = 5x
Substitute for r^2
Converting Rectangular and Parametric Equations
Eliminate the parameter. Find a rectangular equation for the plane curve defined by the parametric equations.
x = 3t, y = t + 7
y = 3x + 7
y = x/3 + 7
y = x/3 - 7
y = 3x - 7
Find a set of parametric equations for the rectangular equation:
y = 2x - 2
x = t/2; y = t - 1
y = 2t; 2x = t + 2
y = 2t2 - 2
x = t; y = 2t - 2
Solution Summary
Converting Rectangular and Parametric Equations is investigated.
x^2 + y^2 = 5x is rectangular form.
Rectangular equation Example 3:
Change r = 5 to rectangular form.
Given that
r =5
r^2 = x^2 + y^2, take square two sides we get r^2.
r^2 = 25
Substitute to rectangular form
x^2 + y^2 = 25
x^2 + y^2 = 25 is the equivalent polar equation to r = 5
Rectangular Equation- more Examples:
Rectangular equation Example 1:
Convert r = 7 cos beta to rectangular form.
Solution:
Since cos = 'x/r' , substitute for cos .
r= 7 * 'x/r'
Multiply two sides by r.
r^2 = 7x
Substitute for r^2.
x^2 + y^2 = 7x is rectangular form.
Rectangular equation Example 2:
Change r = 8 to rectangular form.
Given that
r = 8
r^2 = x^2 + y^2, take square two sides we get r^2.
r^2 = 64
Substitute to rectangular form
x^2 + y^2 = 64
x^2 + y^2 = 64 is the equivalent polar equation to r = 8
