If A−5,0,B5,0 and P moves such that PAPB=21 and maximum area of ΔPAB=1003sq. units then

AB=10⇒PAPB=21≠1Locus of P is a circle(Called as a Apollonius ole) PQ is a diameter.P=53,0;Q=15,0⇒r=203 Max. Area 12.AB.max.height=1210(radius of circle)

If A−5,0,B5,0 and P moves such that PAPB=21 and maximum area of ΔPAB=1003sq. units then

AB=10⇒PAPB=21≠1Locus of P is a circle(Called as a Apollonius ole) PQ is a diameter.P=53,0;Q=15,0⇒r=203 Max. Area 12.AB.max.height=1210(radius of circle)

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If $A (- 5, 0), B (5, 0) and P$ moves such that $\frac{P A}{P B} = \frac{2}{1}$ and maximum area of $Δ P A B = \frac{100}{3} sq.$ units then

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Locus of the point P is a circle

No. of such triangles PAB are 2

No. of such triangles PAB are 4

Locus of the point P is a Parabola

answer is A, C.

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Detailed Solution

$A B = 10 \Rightarrow \frac{P A}{P B} = \frac{2}{1} (\neq 1)$ Locus of P is a circle
(Called as a Apollonius ole) PQ is a diameter.
$P = (\frac{5}{3}, 0); Q = (15, 0) \Rightarrow r = \frac{20}{3}$
Question Image
Max. Area $\frac{1}{2} . A B . \max . h e i g h t = \frac{1}{2} (10)$
(radius of circle)