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Question

A line parallel to the straight line 2x-y=0 is tangent to the hyperbola x24-y22=1 at the point(x1,y1).

Then x12+5y12 is equal to


A

6

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B

10

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C

8

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D

5

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Solution

The correct option is A

6


The explanation for the correct option:

Step 1: Expressing the Given information:

T:xx14-yy12=1..(1)t:2x-y=0T:2x-y=λ..(2)

Step 2: Finding λ

Now, compare (1) and (2)

x1÷42=y1÷21=1λ

x1=8λ,y1=2λ

(x1, y1) lies on hyperbola

(644λ2)-(42λ2)=114=λ2

Step 3:Finding the value of x12+5y12

Now

x12+5y12=(64λ2)+5(4λ2)=(6414)+(2014)=8414=6

∴x12+5y12 is equal to 6

Hence, Option ‘A’ is Correct.


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