Problem 5 Easy Difficulty

Find the equation of the set of points $\mathrm{P}$, the sum of whose distances from $\mathrm{A}(4,0,0)$ and $\mathrm{B}(-4,0,0)$ is equal to $10 .$

Answer

$9x^2+25y^2+25z^2-225=0$

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Calculus 3

NCERT Class 11 - Math

Chapter 12

Introduction to Three Dimensional Geometry

Section 2

Coordinate Axes and Coordinate Planes in Three Dimensional Space

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Problem 5

Video Transcript

in this problem that B B x y Z. We are given that B plus B, B equals to 10. Or I can say that B equals two. 10 minus. Thank you. So he is nothing but x minus four whole square plus Y squared plus said square. This is equals to 10 minus on the roof. Plus four holds work. Uh huh. Last wire square. Yes, that's let's square both sides. We get x minus four whole square plus while square plus. That's what this is something but a minus the whole square. Just a square minus to maybe. Yeah, the script. That square and my square get canceled on both sides. So we are left with This is X -4 whole square minus X plus four. Old square equal. Store 100 minus 20 X-us four whole squad. Last y square. Last that square. This comes as -16 x. Taking Let this be 100 20 X plus four whole square. That's where square, That's Z squared. It has delivered the whole equation by four. This is -4 x. Who's to 25 -5 X plus four whole square. That's why I squared. That's that square. This is nothing about five X plus four. One square plus wire square plus. That's where equal. Stupid. 25 plus four X. It's square board saints. And we get This is 25 X plus four whole square plus Y squared plus. That square is equal. Stop 6 25 plus 16 x square plus. Yes. 200. Thanks on solving it. Further We get nine x square Last 25 Y Square. Just 25. Z sq Minor stood 25 equals to zero which is the required equation. That's all.

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