Question
For the curve , find all the points at which the tangents passes through the origin.
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Text solutionVerified
The equation of the given curve is .
Differentiating w.r.t. , we get
Equation of the tangent at is given by,
....(1)
Since, the tangent passes through the origin (0, 0)
So, equation (1) becomes
.....(2)
Let be the point on the curve at which tangent passes through the orgin.
Slope of the tangent at is .
Slope of the tangent at is .
Equation of the tangent at is given by,
....(1)
Since, the tangent passes through the origin (0, 0)
So, equation (1) becomes
.....(2)
Since, lies on the curve
So , ......(3)
So , ......(3)
From eqn (2) and (3), we get
When .
When .
When .
Hence, the required points are and .
When .
When .
When .
Hence, the required points are and .
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Question Text | For the curve , find all the points at which the tangents passes through the origin. |
Answer Type | Text solution:1 |
Upvotes | 150 |