A point moves so that square of its distance from point (3, -2) is numerically equal to its distance

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9.Straight Line

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A point moves so that square of its distance from the point $(3, -2)$ is numerically equal to its distance from the line $5x - 12y = 13$. The equation of the locus of the point is

A

$13{x^2} + 13{y^2} - 83x + 64y + 182 = 0$

B

${x^2} + {y^2} - 11x + 16y + 26 = 0$

C

${x^2} + {y^2} - 11x + 16y = 0$

D

None of these

Solution

(a) ${(h – 3)^2} + {(k + 2)^2} = \left| {\frac{{5h – 12k – 13}}{{\sqrt {25 + 144} }}} \right|$.

Replace $(h,k)$ by $(x,\,y)$, we get

$13{x^2} + 13{y^2} – 83x + 64y + 182 = 0$, which is the required equation of the locus of the point.

Standard 11

Mathematics

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