Question

# Consider A(0,1) and B(2,0) and P be a point on the line 4x+3y+9=0, co-ordinates of P such is maximum is

Hint:

### The point p should satisfy the line AP and BP then find the lines passing through AP and BP gives point of intersection which is nothing but P.

## The correct answer is:

### Given That:
Consider A(0,1) and B(2,0) and P be a point on the line 4x+3y+9=0, co-ordinates of P such is maximum is
>>> Given:$∣PA−PB∣$ is maximum.
>>> A line passes through $P$ having the equation $4x+3y+9=0$
>>> Maximum value of $∣PA−PB∣=∣AB∣$
>>> Equation of the line $AB=y−0=2−00−1 (x−0)$
$⇒2y=−x$ or $x+2y=0$
>>> The intersection of the lines $x=−2y$ and $4x+3y+9=0$ is
$4×−2y+3y+9=0$
$⇒−8y+3y=−9$
$⇒−5y=−9$
$⇒y= $
$∴x=−2y=−2×= $
>>> Hence the point is (, ).

Hence the point is (, ).

### Related Questions to study

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P1 = 1;

P2 = ;

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