How do you name the curve given by the conic

dohtarjev510 2022-02-10 Answered
How do you name the curve given by the conic r=41+cosθ?
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Expert Answer

s3au1d8wh
Answered 2022-02-11 Author has 11 answers

Convert to the General Cartesian Form:
Ax2+Bxy+Cy2+Dx+Ey+F=0
Compute the determinant:
Δ=B24AC
If Δ<0, then it is an ellipse or a circle. If B=0and A=C, then it is a circle. Otherwise, it is an ellipse.
If Δ=0, then it is a parabola.
If Δ>0, them it is a hyperbola.
Given: r=41+cos(θ)
r+rcos(θ)=4
Substitute r=x2+y2and rcos(θ)=x:
x2+y2+x=4
x2+y2=4x
x2+y2=x28x+16

y2+8x16=0
Please observe that, for the the above equation, the coefficients of the General Cartesian Form are, A=B=E=0,C=1,D=8,and F=16
Δ=024(0)(1)=0
It is a parabola.

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