1. The point on the ellipse 16x² +9y2 = 400, at
which the ordinate decreases at the same rate
at which the abscissa increases is
Answers
Answered by
1
Step-by-step explanation:
16x
2
+9y
2
=400
Differentiating w.r.t time, we get
32x
dt
dx
+18y
dt
dy
=0
Given that the ordinate decrease at the same rate as the abscissa increases,
dt
dy
=
dt
−dx
⇒32x=18y or 16x=9y
Substituting x=
16
9y
in the equation, we get
16×
16
9y
×
16
9y
+9y
2
=400
⇒y
2
(
16
81
+9)=400
⇒y
2
=
81+9×16
400×16
∴y
2
=
225
400×16
=
9
256
∴y=±
3
16
Correspondingly, x=±3
∴ the points are (3,
3
16
),(−3,
3
−16
)
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