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.

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Ella 3 weeks 2021-10-04T02:31:35+00:00 1 Answer 0 views 0

Answers ( )

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    2021-10-04T02:32:42+00:00

    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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