Question

The tangent to the curve y = 6√(x) at the point (4, 12) meets the axes at A & B. Show the the distance AB may be written in the form k √(13) and state the value of k.
The answer is,k=2​

Answer 1

Step-by-step explanation:

(y−y1)=f′(x1)

y−y1=f′(x1)(x−x1)

y=0,f′(x1)−y=x−x1

⇒x=x1=f′(x1)y1

A=(x1−f′(x1)y1,0)

x=0,y−y1=f′(x1)⋅(−x1)

⇒y=y1−x1f′(x1)

B=(

P divides AB in ratio 1:3

∴

x1=43(x1−f′(x1)y1)

y1=4y1−x1f′(x1)

4y1=y1x1f′(x1)

f′(x1)=x1−3y1

f′(x)=x−3y

dxdy=x−3y

ydy=x−3dx

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