Please check:
1.Find polar equation of x^2 + y^2 = 10y
subbed r^2 for x^2 + y^2 and sin(theta sin for y
=r^2=10sin(theta)
2. y=5
r=5/sin
3. x^2+y^2
=x^2 + y^2 =2x+3y
1. r² = 10r sin θ
r = 10 sin θ
2. looks good
3. r² = 2rcosθ + 3rsinθ
r = 2cosθ + 3sinθ
1. To find the polar equation of the equation x^2 + y^2 = 10y, you can substitute r^2 for x^2 + y^2 and sin(theta) for y.
Start with the equation x^2 + y^2 = 10y.
Substitute r^2 for x^2 + y^2:
r^2 = 10y
Then, substitute sin(theta) for y:
r^2 = 10*sin(theta)
So, the polar equation of x^2 + y^2 = 10y is r^2 = 10*sin(theta).
2. To find the value of r when y = 5, you need to substitute y = 5 in the polar equation.
Start with the polar equation r^2 = 10*sin(theta).
Substitute y = 5:
r^2 = 10*sin(theta)
Simplify if necessary, and you'll get r = sqrt(10)*sin(theta) or r = -sqrt(10)*sin(theta).
3. To find x^2 + y^2 when x^2 + y^2 = 2x + 3y, you can directly substitute the given equation.
Start with the equation x^2 + y^2 = 2x + 3y.
So, x^2 + y^2 = 2x + 3y.