Question

# If the tangent at the point on the curve meets the curve again at

Hint:

### We are give the point of tangency. It is (at^{2}, at^{3}). The given curve is. We have to find the point where tangent intersects the curve again. We will find the slope using the curve. Then, we will use two point form to find the point.

## The correct answer is:

### The given curve is ay^{2} = x^{3}

The point of tangency is (at^{2}, at^{3})

Let the point that tangent intersects again be (as^{2}, as^{3})

We can find the slope of tangent by differentiating the given curve w.r.t x

Now, we will use two point form to solve the question.

If (x_{1}, y_{1}) and (x_{2}, y_{2}) be two points on the line then the slope is

For this question, it will be

We will solve it further and find the value.

(s - t) = 0

s = t

It means the same point of tangency. We want to find different point.

(2s + t) = 0

s =

So, the point will be

This is the required answer.

For such questions, we should know the formulas to find slope.

### Related Questions to study

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