# Given the family of lines, #a(3x+4y+6) + b(x+y+2)=0#. The line of the family situated at the greatest distance from the point #P(2,3)# has the equation?

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Ans: #4x+3y + 8 = 0#

Ans:

##### 1 Answer

#### Explanation:

Let **family of lines.**

Observe that, **both** **can not be simultaneously zero.**

So, if **dividing** the **equation** of the **family** by

The

Since to **maximise** **same as to maximise**

we must have the **denominator** **minimum.**

Now,

For this **reqd. line** from the **family**

Recall that the **above** has been derived on the **assumption** that,

If we **work out assuming** that **reqd. line**

happens to be

To **determine** which of the lines **fulfills** the

**given condition** , we finally have to work out the

from

Consequently, **desired line!**