solve x^2d^2y/dx^2-3xdy/dx+y=sin(logx)/x
Answers
Explanation:
∴Center=(7,−5)
\green{\tt{\therefore{Vertices=(7,-13)\:and\:(7,3)}}}∴Vertices=(7,−13)and(7,3)
\green{\tt{\therefore{Foci=(7,\pm2\sqrt{41}-5)}}}∴Foci=(7,±2
41
−5)
\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}
Step−by−stepexplanation:
\begin{gathered}\green{\underline \bold{Given :}} \\ \tt: \implies 16 {x}^{2} - 224x + 25 {y}^{2} + 250y - 191 = 0 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Center = ?\\ \\ \tt: \implies Foci=? \\ \\ \tt: \implies Vertices =? \\ \\ \tt: \implies Co-vertices =?\end{gathered}
Given:
:⟹16x
2
−224x+25y
2
+250y−191=0
ToFind:
:⟹Center=?
:⟹Foci=?
:⟹Vertices=?
:⟹Co−vertices=?
•
:⟹16x
2
−224x+25y
2
+250y−191=0
:⟹(4x)
2
+28
2
−224x−28
2
+(5y)
2
+25
2
+250y−25
2
−191=0
:⟹(4x−28)
2
+(5y+25)
2
=191+625+784
:⟹(4x−28)
2
+(5y+25)
2
=1600
:⟹
1600
(4x−28)
2
+
1600
(5y+25)
2
=1
:⟹
1600
16(x−7)
2
+
1600
25(y+5)
2
=1
:⟹
100
(x−7)
2
+
64
(y+5)
2
=1
:⟹
10
2
(x−7)
2
+
8
2
(y+5)
2
=1
\
:⟹
a
2
X
2
+
b
2
Y
2
=1
Asweknowthat
:⟹x=0
:⟹x−7=0
:⟹x=7
:⟹Y=0
:⟹y+5=0
:⟹y=−5
∴Center(7,−5)
Asweknowthat
:⟹X=0
:⟹x−7=0
:⟹x=7
:⟹Y=±b
:⟹y+5=±8
:⟹y=−13and3
∴Vertex(7,−13)and(7,3)
Asweknowthat
:⟹a
2
=b
2
(e
2
−1)
:⟹100=64(e
2
−1)
:⟹
64
100
=e
2
−1
:⟹
16
25
+1=e
2
:⟹e=
4
41
Asweknowthat
:⟹x=7
:⟹Y=±be
:⟹y+5=±8×
4
41
:⟹y+5=±2
41
:⟹y=±2
41
−5
∴Foci(7,±2
41
−5)