Question

What is the standard form of the ellipse equation

25x2 - 150x + 9y2 = 0?
O
(x - 3)2
32
y
1
+
52
0 (x - 5)
1
y2
22
(y - 3)2
22
0x2
+
14
1
O
x2
32
(y - 3)2
22
= 1

Answer 1

Answer: The correct answer is in the first option.

Explanation:

Equation of an Ellipse

`(x^(2) )/(a^(2) ) +(y^(2) )/(b^(2) ) =1\\\\25x^(2) - 150x + 9y^(2) = 0\\\\\text {Let's \: perform \: the \: transformations:}\\\\(25x^(2) )/(25 \cdot 9) -(150x)/(25 \cdot 9) +(9y^(2) )/(25 \cdot 9) =0\\\\(x^(2) )/(3^(2) ) -(6x)/(3^(2) ) +(y^(2) )/(5^(2) ) =0\\\\(x^(2) -6x)/(3^(2) ) +(y^(2) )/(5^(2) ) +(3^(2) )/(3^(2) ) -(3^(2) )/(3^(2) ) =0\\\\(x^(2) -6x+3^(2) )/(3^(2) ) +(y^(2) )/(5^(2) ) =(3^(2) )/(3^(2) )`

`((x-3)^(2) )/(3^(2) ) +(y^(2) )/(5^(2) ) =1`