Question
Rewrite the parametric equations
9x2+4y2=1
Evaluate
{x=3sin(t)y=2cos(t)
Transform the expression
{9x2=sin2(t)4y2=cos2(t)
Transform using a trigonometric identity
{9x2=sin2(t)4y2=1−sin2(t)
Choose the parametric equation
9x2=sin2(t)
Rewrite the expression
sin2(t)=9x2
Substitute the given value of sin2(t)=9x2 into the equation 4y2=1−sin2(t)
4y2=99−x2
Rewrite the expression
41y2=1−91x2
Move the expression to the left-hand side and change its sign
41y2−(−91x2)=1
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
41y2+91x2=1
Use the commutative property to reorder the terms
91x2+41y2=1
Use a=a11 to transform the expression
9x2+41y2=1
Solution
9x2+4y2=1
Show Solution
Find the first derivative
dxdy=−3cos(t)2sin(t)
Evaluate
{x=3sin(t)y=2cos(t)
To find the derivative dxdy,first find dtdx and dtdy
dtd(x)=dtd(3sin(t))dtd(y)=dtd(2cos(t))
Find the derivative
More Steps
Evaluate
dtd(x)=dtd(3sin(t))
Calculate the derivative
More Steps
Evaluate
dtd(x)
Use differentiation rules
dxd(x)×dtdx
Use dxdxn=nxn−1 to find derivative
dtdx
dtdx=dtd(3sin(t))
Calculate the derivative
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Evaluate
dtd(3sin(t))
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
3×dtd(sin(t))
Use dxd(sinx)=cosx to find derivative
3cos(t)
dtdx=3cos(t)
dtdx=3cos(t)dtd(y)=dtd(2cos(t))
Find the derivative
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Evaluate
dtd(y)=dtd(2cos(t))
Calculate the derivative
More Steps
Evaluate
dtd(y)
Use differentiation rules
dyd(y)×dtdy
Use dxdxn=nxn−1 to find derivative
dtdy
dtdy=dtd(2cos(t))
Calculate the derivative
More Steps
Evaluate
dtd(2cos(t))
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
2×dtd(cos(t))
Use dxd(cosx)=−sinx to find derivative
2(−sin(t))
Calculate
−2sin(t)
dtdy=−2sin(t)
dtdx=3cos(t)dtdy=−2sin(t)
Solution
dxdy=−3cos(t)2sin(t)
Show Solution