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Question

The equation x-52+x-5y-6-2y-62=0 represents


A

A circle

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B

Two straight lines passing through the origin

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C

Two straight lines passing through the point (5,6)

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D

None of these

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Solution

The correct option is C

Two straight lines passing through the point (5,6)


Explanation for the correct option:

Step 1: Simplify the given equation.

An equation x-52+x-5y-6-2y-62=0 is given.

Simplify the given equation as follows:

x-52+x-5y-6-2y-62=0⇒x-52+x-5y-6+x-5y-6-x-5y-6-2y-62=0⇒x-52+2x-5y-6-x-5y-6-2y-62=0⇒(x-5)x-5+2y-6-y-6x-5+2y-6=0⇒(x-5)x+2y-17-y-6x+2y-17=0⇒x-y+1x+2y-17=0

So, the given line represents the pair of straight lines x-y+1=0 and x+2y-17=0.

Step 2: Find the point of intersection of both lines.

Since, x-y+1

Therefore, x=y-1...1

Also, x+2y-17=0...2

From equation 1 and equation 2, we get

y-1+2y-17=0⇒3y=18⇒y=6

Now, substitute y=6 in equation 1 and solve for x.

x=6-1⇒x=5

Therefore, the point of intersection is (5,6).

That is, the equation x-52+x-5y-6-2y-62=0 represents a pair of straight lines passing through the point (5,6).

Hence, the option C is correct.


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