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Chapter 11: Q. 95 (page 775)

Use Descartes鈥檚 method to find the equation of the line tangent to the graph 2x2+3y2=14at the given point (1,2).

Short Answer

Expert verified

Equation of tangent is y=-13x+73

Step by step solution

01

Step 1. Given information  

2x2+3y2=14 we have to find tangent at (1,2)

02

Step 2. General equation of tangent Now we put b=2-m  y=mx +bWe get

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

y=mx +b

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

2-m=b

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

We gety=mx+(2-m)

03

Step 3. Calculations 

Now put y=mx+(2-m) in 2x2+3y2=14

We get

2x2+3(mx+2-m)2=14 2x2+3m2x2+6mx-3m2x+6mx+12-6m-3m2x-6m+3m2=142+3m2x2+12m-6m2x+3m2-12m-2-0

04

Step 3. Solving the quadratic equation

Now we have to solve the quadratic equation . we get

x=6m2-12m卤6m2-12m2-42+3m23m2-12m-222+3m2

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

(6m2-12m2-42+3m23m2-12m-2=0(3m+1)2=0m=-13

05

Step 5. Equation of tangent

Now put m=-13in equation of tangent y=mx+(2-m)

We get

y=-13x+73


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