Find points on the curve at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis. Question Find points on the curve at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis. in progress 0 Math Ella 3 weeks 2021-10-04T02:31:35+00:00 2021-10-04T02:31:35+00:00 1 Answer 0 views 0

## Answers ( )

Answer:The equation of the given curve is.

x^2/9+y^2/16=1

On differentiating both sides with respect to x, we have:

2x/9+2y/16*dy/dx=0

dx/dy=-16x/9y

(i) The tangent is parallel to the x-axis if the slope of the tangent is i.e., 0

-16x/9y=0

which is possible if x = 0.

then,x^2/9+y^2/16=1

Then,for x = 0

y^2=16

y=.± 4

Hence, the points at which the tangents are parallel to the x-axis are

(0, 4) and (0, − 4).

(ii) The tangent is parallel to the y-axis if the slope of the normal is 0, which gives⇒ y = 0.

-1/(-16x/9y)=9y/16x=0

y=0

then ,x^2/9+y^2/16=1

,for y =0

x=. ± 3

Hence, the points at which the tangents are parallel to the y-axis are

(3, 0) and (− 3, 0).

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