Respuesta :
Answer:
The equation of an ellipse is [tex]\frac{x^{2} }{289} + \frac{y^{2} }{225} = 1[/tex] and the vertical width of ellipse at x = 6 inch from centre of ellipse is 28.06 inch.
Step-by-step explanation:
We know that, the equation of an ellipse with horizontal major axis with centre at (0,0):
[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } = 1[/tex] ------------------------------------(1)
According to the question,
[tex]a = \frac{34}{2} = 17[/tex] inch⇒[tex]a^{2} = 17^{2} = 289[/tex]
[tex]b = \frac{30}{2} = 15[/tex] inch⇒[tex]b^{2} = 15^{2} = 225[/tex]
After putting the value of [tex]a^{2}[/tex] and [tex]b^{2}[/tex] in the equation(1), we get
The equation of an ellipse is [tex]\frac{x^{2} }{289} + \frac{y^{2} }{225} = 1[/tex]
[tex]\frac{y^{2} }{225} = 1- \frac{x^{2} }{289}[/tex]
⇒[tex]y^{2} = (1-\frac{y^{2} }{289} )\times225[/tex]
⇒[tex]y = \sqrt{(1-\frac{x^{2} }{289})\times225 }[/tex]-----------------------------(2)
At [tex]x = 6[/tex] inch from centre(0,0) of ellipse,
[tex]y = \sqrt{( 1- \frac{6^{2} }{289})\times225 }[/tex]
⇒[tex]y = 14.03[/tex] inch
Therefore, the total vertical width of ellipse at x = 6 inch from centre of ellipse = [tex]2\times14.03[/tex] = 28.06 inch
