﻿ If a (2,0) and (0,2) are given points and p is a point such that PA:PB = 2:3 then the locus of p passes through the point (a,a) for : Kaysons Education

If A (2,0) And (0,2) Are Given Points And p is A Point Such That PA:PB = 2:3 Then The Locus Of p passes Through The Point (a,a) For

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Question

Solution

Correct option is

No real value of a

Let p(x, y) be such that PA:PB = 2:3

Then

9(PA)2 = 4(PB)2

⇒ 9[(x – 2)y2] = 4[x2 + (y – 2)2]

⇒ 9(x2 + y2 – 4x +4) = 4(x2 + y2 – 4x + 4)

⇒ 5x + 5y 2 – 36x  + 16y + 20 = 0

Which is the locus of p and it passes through (a,a)if

5a2 + 5a2 – 36a + 16a + 20 = 0

10a2 – 20a + 20 = 0

(a – 1)2 + 1= 0

Which is not possible for any real value of a.

SIMILAR QUESTIONS

Q1

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Q2

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Q3

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Q4

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Q5

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Q6

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Q7

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Q8

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Q9

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Q10

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