Find The Equation Of The Straight Line Through The Point P(a, b) Parallel To The Lines . Also Find The Intercepts Made By It On The Axes.

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Question

Find the equation of the straight line through the point P(a, b) parallel to the lines . Also find the intercepts made by it on the axes.

diffcult

Solution

Correct option is

2a and 2b

Let the line

meets the axes in A and B respectively.

So that

OA = a, OB = b

Let the required parallel line meet in A’ and B’ respectively, so thet

OA’ = a’ and OB’ = b’

∴ Equation of required line is

Since âˆ†’s OAB and OA’B’ are similarly, then

.

Substituting these values in eq. (i) then

It passes through (a, b) then

.

From (ii) required equation is

Evidently intercepts on the axes are 2a and 2b.

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