First slide

Pair of straight lines

Question

Let $A, B$ be the feet of the perpendiculars drawn from $C (1, 1)$ to the pair of lines $7 x^{2} - 20 xy + 12 y^{2} = 0$ . If P is the midpoint of $OC$ then $PA + PB =$

Moderate

A

$\sqrt{2}$
B

$2 \sqrt{2}$
C

2
D

4

Solution

Given be the foot of the perpendiculars draw from the point $C (1, 1)$ to the pair of lines $7 x^{2} - 20 xy + 12 y^{2} = 0$
The points $A, B$ lies on the circle whose diameter end points are $O, C$
Hence, $OP = PC = radius$
Therefore, $PA = PB = \frac{OC}{2} = \frac{\sqrt{2}}{2}$
It implies that $PA + PB = \sqrt{2}$

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