Question

Find the equation of the locus of a point which moves
such that the ratio of its distance from the origin and
the point A(-2,5) is 2 : 3.


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⚫️Explanationrequired ​

Answer 1

Let the point whose locus is to be determined to be (h,k)

Distance of (h,k) from (2,0) =

Distance of (h,k) from (1,3) =

According to the question:

Squaring both sides:

16{(h - 2)2 + k2 } = 25{(h - 1)2 + (k - 3)2 }

⇒ 16{h2 + 4 - 4h + k2 } = 25{h2 - 2h + 1 + k2 - 6k + 9}

⇒ 9h2 + 9k2 + 14h - 150k + 186 = 0

Replace (h,k) with (x,y)

Thus, the locus of a point which moves such that the ratio of its distance from (2, 0) and (1, 3) is 5 : 4 is –

9x2 + 9y2 + 14x - 150y + 186 = 0 ….ans

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