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find the equation of locus of p which distance is A:B in ratio 2:3

Asked by lohitaashw.neerella | 30 Jun, 2022, 09:22: PM

Expert Answer

Question: Find the equation of locus of P, if the ratio of the distance from P to (5,−4) and (7,6) is 2:3.

Solution:

Let P(x, y), A(5,−4) and B(7,6)

Distance space of space straight P space from space left parenthesis 5 comma space minus 4 right parenthesis space equals square root of open parentheses straight x minus 5 close parentheses squared plus left parenthesis straight y plus 4 right parenthesis squared end root Distance space of space straight P space from space left parenthesis 7 comma space 6 right parenthesis space equals square root of open parentheses straight x minus 7 close parentheses squared plus left parenthesis straight y minus 6 right parenthesis squared end root Since comma space AP colon PB equals 2 colon 3 rightwards double arrow fraction numerator square root of open parentheses straight x minus 5 close parentheses squared plus left parenthesis straight y plus 4 right parenthesis squared end root over denominator square root of open parentheses straight x minus 7 close parentheses squared plus left parenthesis straight y minus 6 right parenthesis squared end root end fraction equals 2 over 3 rightwards double arrow 9 left parenthesis straight x minus 5 right parenthesis squared plus 9 left parenthesis straight y plus 4 right parenthesis squared equals 4 left parenthesis straight x minus 7 right parenthesis squared plus 4 left parenthesis straight y minus 6 right parenthesis squared space rightwards double arrow 9 straight x squared minus 90 straight x plus 225 plus 9 straight y squared plus 72 straight y plus 144 equals 4 straight x squared minus 56 straight x plus 196 plus 4 straight y squared plus 144 minus 48 straight y space rightwards double arrow 5 straight x squared plus 5 straight y squared minus 34 straight x plus 120 straight y plus 31 equals 0

Answered by Renu Varma | 04 Jul, 2022, 10:52: AM

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