Mathematics - Circle Question with Solution | TestHub

MathematicsCircleFamily of circlesMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For Q37-39: A=(0,0), B=(4,0), and P moves so that PA=K·PB, where K>0 and K≠1. Its locus is a circle S meeting AB at D and E. In Q37, a separate circle centered at (3,2) touches AB at D.

$A = (0, 0), B = (4, 0)$ and $P$ varies with $P A = K PB (K > 0, K \neq = 1)$ . Its locus is a circle $S$ , meeting $A B$ at $D, E$ . If a circle with centre $(3, 2)$ touches the line $A B$ at $D$ , then $E$ is

Options:

Answer:

Solution:

The separate circle centred at $(3, 2)$ touches $A B$ at $D = (3, 0)$ . Thus $D A / D B = 3$ , giving $K = 3$ . On line $A B$ , the other solution of $∣ x ∣ = 3∣ x - 4∣$ is $E = (6, 0)$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Family of circles

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