Please answer question 6 on the screenshot in the post. Please give a full explanation of each of the steps. ExercisesAFor Exercises 1-4, find the (a) cylindrical and (b) spherical coordinates of the point whoseCartesian coordinates are given.1. (2,2v3, –1)2. (-5,5,6)3. (v21, – v7,0)4. (0, v2,2)For Exercises 5-7, write the given equation in (a) cylindrical and (b) spherical coordinates.5. x² + y² +z² = 256. x² + y² = 2y7. x² + y2 + 9z² = 36B8. Describe the intersection of the surfaces whose equations in spherical coordinates are0 = 5 and ø =4.9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes asphere centered at (a,0,0) with radius |a|.

6. Consider the equation x2+y2=2y. (a) Cylindrical coordinates: The relation between cartesian coordinates x,y,z and cylindrical coordinates r,θ,z are given by x=rcosθy=rsinθz=z Therefore, x2+y2=rcosθ2+rsinθ2=r2cos2θ+r2sin2θ=r2cos2θ+sin2θ=r21 since cos2θ+sin2θ=1=r2 and 2y=2rsinθ. Substitute the equations x2+y2=r2 and 2y=2rsinθ in x2+y2=2y and simplify as follows. x2+y2=2y⇒r2=2rsinθ⇒r2r=2rsinθr⇒r=2sinθ Hence, the given equation in cylindrical coordinates is r=2sinθ.(b) Spherical coordinates: The relation between cartesian coordinates x,y,z and spherical coordinates ρ,θ,ϕ are given by x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ Therefore, x2+y2=ρsinϕcosθ2+ρsinϕsinθ2=ρ2sin2ϕcos2θ+ρ2sin2ϕsin2θ=ρ2sin2ϕcos2θ+sin2θ=ρ2sin2ϕ1 since cos2θ+sin2θ=1=ρ2sin2ϕ and 2y=2ρsinϕsinθ. Substitute the equations x2+y2=ρ2sin2ϕ and 2y=2ρsinϕsinθ in x2+y2=2y and simplify as follows. x2+y2=2y⇒ρ2sin2ϕ=2ρsinϕsinθ⇒ρ2sin2ϕρsinϕ=2ρsinϕsinθρsinϕ⇒ρsinϕ=2sinθ Hence, the given equation in spherical coordinates is ρsinϕ=2sinθ.