Question

The equation to the locus of a point P for which the distance from P to ( 4, 0) is double the distance from P
to x - axis is​

Answer 1

we have to find the equation of the locus of a point P for which the distance from P to (4,0) is double the distance from P to x - axis.

solution : let point P(x , y) and point on x - axis = (x, 0)

A = (4, 0) and B = (x, 0)

from distance formula,

distance between P and A = √{(x - 4)² + y²}

distance between P and B - axis = √{(x - x)² + (y - 0)²} = |y|

a/c to question,

PA = 2PB

⇒√{(x - 4)² + y²} = 2|y|

squaring both sides we get,

⇒(x - 4)² + y² = 4y²

⇒(x - 4)² - 3y² = 0

⇒x² - 3y² - 8x + 16 = 0

Therefore the locus of point P is x² - 3y² - 8x + 16.

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Answer 2

Answer:

hope you find the attachment