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Eqn of Locus calculation

Eqn of Locus calculation

by Sinjan Jana -
Number of replies: 2

The question is :

The sum of the distance of P(x,y) from (4,0) and (-4,0) is 10. Find the equation of locus.

Alright, I actually understand the logic of the problem, but the problem is that, I am stuck in an calculation. The calculation might be easy, but at this point of time I am not able to go about it. So plz help me to calculate.

Using the condition, The relation I get is

\(\sqrt{(x~-~4)^2+y^2}~+~\sqrt{(x~+~4)^2+y^2}~=~10\)

But using the above relation how do I proceed to the final answer?? Please give me the steps and if there are any other mistake, then plz clarify it.

The final answer given is :

\(9x^2~+~25y^2~=~225\)

Thnxx..!!

In reply to Sinjan Jana

Re: Eqn of Locus calculation

by Manish Verma -

When you want to get rid of roots in an equation of the type:

\(\sqrt {Expression1}+\sqrt {Expression2}\)=k

Then keep one of the roots on one side and then square.

After squaring you may still end up with one root.

Now, keep that root alone on one side and square again.

In reply to Manish Verma

Re: Eqn of Locus calculation

by Sinjan Jana -
Thank you very much for help sir.. I got it.. I should have had more patience.