Answers>Further Mathematics>A Level>Article

What is the polar form of the equation: x^2+y^2 =xy+1

Using Pythagoras, x² + y² = r².Using basic trigonometry, x = rsinθ and y = rcosθ.
xy + 1 = r²sinθcosθ + 1 = (1/2)r²sin2θ + 1
Subbing in both halves and doubling gives:2r² = r²sin2θ + 2
-> r²(2 - sin2θ)r² = 2
-> r²= 2/(2-sin2θ)

Answered by Hansen W. • Further Mathematics tutor

5835 Views

See similar Further Mathematics A Level tutors

What is the polar form of the equation: x^2+y^2 =xy+1

Related Further Mathematics A Level answers

Find the cube roots of unity.

Prove that (AB)^-1 = B^-1 A^-1

Given that z = a + bj, find Re(z/z) and Im(z/z).

Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

What is the polar form of the equation: x^2+y^2 =xy+1

Related Further Mathematics A Level answers

Find the cube roots of unity.

Prove that (AB)^-1 = B^-1 A^-1

Given that z = a + bj, find Re(z/z*) and Im(z/z*).

Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

Given that z = a + bj, find Re(z/z) and Im(z/z).