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Chapter 11: Q. 97 (page 775)

Use Descartes鈥檚 method to find the equation of the line tangent to the graph x2-y2=3at the given point (2,1).

Short Answer

Expert verified

Equation of tangent is y=2x-3

Step by step solution

01

Step 1. Given information  

x2-y2=3 we have to find tangent at (2,1)

02

Step 2. General equation of tangent 

As we know that the equation of the tangent line is in the form of

y=mx +b

As this line is passes through (2,1) So we get

1-2m=b

Now we put b=1-2m y=mx +b

We get

y=mx+(1-2m)

03

Step 3. Calculations 

Now put y=mx+(1-2m)in x2-y2=3

We get

x2-(mx+1-2m)2=3 Nowweget1-m2x2+4m2-2mx-4m2+4m-4=0

04

Step 3. Solving the quadratic equation 

Now we have to solve the quadratic equation . we get

x=2m-4m2卤4m2-2m2-41-m2-4m2+4m-421-m2

Now we want the unique solutions for this both the roots should be equal .So

4m2-2m2-41-m2-4m2+4m-4=0m2-4m+4=0m-2=0m=2

05

Step 5. Equation of tangent

Now put m=2 in equation of tangent y=mx+(1-2m)

We get

y=2x-3


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