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Joint Entrance Examination
Mathematics
Differential Equations
Question 323
Question 323 of 490
Medium
MCQ
The normal to
y
=
y
(
x
)
y=y(x)
y
=
y
(
x
)
at
P
(
x
,
y
)
P(x,y)
P
(
x
,
y
)
meets the
x
x
x
-axis at
G
G
G
. If
O
G
=
2
⋅
(
abscissa of
P
)
OG=2\cdot(\text{abscissa of }P)
O
G
=
2
⋅
(
abscissa of
P
)
, the curve is a:
A
circle
B
hyperbola
C
ellipse
D
parabola
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Official solution
X
G
=
x
+
y
d
y
d
x
=
2
x
⟹
y
d
y
d
x
=
x
⟹
y
2
−
x
2
=
X_G = x+y\dfrac{dy}{dx} = 2x \implies y\dfrac{dy}{dx}=x \implies y^2-x^2=
X
G
=
x
+
y
d
x
d
y
=
2
x
⟹
y
d
x
d
y
=
x
⟹
y
2
−
x
2
=
const --- a hyperbola.
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