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If a> 0 and...

Question

If $a > 0$ and $P (- a, 0), Q (a, 0)$ and $R (1, 1)$ are three points such that $∣ ∣ (P R)^{2} - (Q R)^{2} ∣ ∣ = 12,$ then

(P R)^{2} = 17

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(Q R)^{2} = 5

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(P R)^{2} = 5

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(Q R)^{2} = 17

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Solution

The correct options are
A $(P R)^{2} = 17$
B $(Q R)^{2} = 5$
$| {(1 + a)}^{2} + 1 - [{(1 - a)}^{2} + 1] | = 12$
$| 4 a | = 12$
$4 a = 12$ or $4 a = - 12$
$∴ a = 3, - 3$
Since $a > 0$
$∴ a = 3$
Now ${(P R)}^{2} = {(1 + 3)}^{2} + 1$
${(P R)}^{2} = 17$
${(Q R)}^{2} = {(1 - 3)}^{2} + 1$
${(Q R)}^{2} = 5$

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