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Question
Mathematics
Let P(x, y) be a variable point on the curve 4 x2+9 y2-8 x-36 y+15=0, then min .(x2-2 x+y2-4 y+5)+ max .(x2-2 x+y2-4 y+5) is equal to
Q. Let
P
(
x
,
y
)
be a variable point on the curve
4
x
2
+
9
y
2
−
8
x
−
36
y
+
15
=
0
, then
min
.
(
x
2
−
2
x
+
y
2
−
4
y
+
5
)
+
max
.
(
x
2
−
2
x
+
y
2
−
4
y
+
5
)
is equal to
62
125
Conic Sections
Report Error
A
325
36
B
13
25
C
25
13
D
36
325
Solution:
We have,
4
25
(
x
−
1
)
2
+
9
25
(
y
−
2
)
2
=
1
So,
min
.
(
(
x
−
1
)
2
+
(
y
−
2
)
2
)
=
9
25
and
max
⋅
(
(
x
−
1
)
2
+
(
y
−
2
)
2
)
=
4
25
.