Question

The Length of sub tangent at any point P on y = x³ is 2. Find the coordinate of point P

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Answer 1

ANSWER :

GIVEN :

• y = x³
• Length of sub tangent = 2

TO FIND :

• Coordinate of point P

SOLUTION :

Let the point be P(h,k)

=> y = x³ ____ (1)

Differentiating both sides w.r.t x,

=> dy/dx = 3x

=> dx/dy = 1/3x ____ (2)

We know, Length of Sub tangent = y. dx/dy

Length of Sub tangent = x³(1/3x) {From (1) & (2)}

• Length of Sub tangent = x²/3

At point P(h,k)

(x,y) ----- (h,k)

• Length of Sub tangent = h²/3

=> 2 = h²/3

=> h² = 6

=> h = √6 or h = -√6

Now, k = h³

• (When h = √6)

k = √6³

k = 6√6

• (When h = -√6)

k = (-√6)³

k = -6√6

• Therefore, the point P(h,k) is (√6, 6√6) or (-√6, -6√6)

Answer 2

Step-by-step explanation:

ANSWER :

GIVEN :

y = x³

Length of sub tangent = 2

TO FIND :

Coordinate of point P

SOLUTION :

Let the point be P(h,k)

=> y = x³ ____ (1)

Differentiating both sides w.r.t x,

=> dy/dx = 3x

=> dx/dy = 1/3x ____ (2)

We know, Length of Sub tangent = y. dx/dy

Length of Sub tangent = x³(1/3x) {From (1) & (2)}

Length of Sub tangent = x²/3

At point P(h,k)

(x,y) ----- (h,k)

Length of Sub tangent = h²/3

=> 2 = h²/3

=> h² = 6

=> h = √6 or h = -√6

Now, k = h³

(When h = √6)

k = √6³

k = 6√6

(When h = -√6)

k = (-√6)³

k = -6√6

Therefore, the point P(h,k) is (√6, 6√6) or (-√6, -6√6)