To 2 decimal places, what is the value of d?

Question

An ellipse has equation ax²+by²=c where a = 20, b = 45 and c = 232. One of the vertices, (0, d), lies on the positive y-axis. To 2 decimal places, what is the value of d?

Answer 1

20x² + 45y² = 232

 

 

Divide both sides of the equation by 232.

 

(x² / 0.086) + (y² / 0.194) = 1

 

 

Since we want the positive y-axis, we focus on the y²/0.194 term.

 

d = √(0.194)

 

 

In general,

 

d = √(b / c)