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प्रश्न
Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.
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उत्तर
We have P(x, y), Q(-3, 0) and R(3, 0)
`PQ = sqrt((x + 3)^2 + (y - 0)^2)`
`=> 4 = sqrt(x^2 + 9 + 6x + y^2)`
Squaring both sides
`=> (4)^2 = (sqrt(x^2 + 9 + 6x + y^2))`
`=> 16 = x^2 + 9 + 6x + y^2`
`=> x^2 + y^2 = 16 - 9 - 6x`
`=> x^2 + y^2 = 7 - 6x` ......(1)
`PR = (sqrt((x - 3)^2 + (y - 0)^2)`
`=> 4 = sqrt(x^2 + 9 - 6x + y^2)`
Squaring both sides
`(4)^2 = (sqrt(x^2 + 9 - 6x + y^2))`
`=> 16 = x^2 + 9 - 6x + y^2`
`=> x^2 + y^2 = 16 - 9 + 6x`
`=> x^2 + y^2 = 7 + 6x` .....(2)
Equating (1) and (2)
7 - 6x = 7 + 6x
⇒ 7 - 7 = 6x + 6x
⇒ 0 = 12x
⇒ x = 0
Substituting the value of x = 0 in (2)
`x^2 + y^2 = 7 + 6x`
`0 + y^2 = 7 + 6 xx 0`
`y^2 = 7`
`y = +- sqrt7`
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