Question

Locus of a point such that the sum of its distance from the points (0, 2) and (0, -2) is 6

• A. $4x^2+6y^2=5$
• B. $5x^2+9y^2=50$
• C. $9x^2+5y^2=45$
• D. None

Answer 1

The correct option is C $9x^2+5y^2=45$

$Solution-Weshallusedistanceformulad=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}toobtainAP,BP.AP=\sqrt{{(x-0)}^2+{(y-2)}^2}=andBP=\sqrt{{(x-0)}^2+{(y+2)}^2}.NowAP-BP=6\sqrt{{(x-0)}^2+{(y-2)}^2}+\sqrt{{(x-0)}^2+{(y+2)}^2}=6⟹\sqrt{{(x-0)}^2+{(y-2)}^2}=6-\sqrt{{(x-0)}^2+{(y+2)}^2}⟹x^2+{(y-2)}^2=36+x^2+{(y+2)}^2-12\sqrt{{(x-0)}^2+{(y+2)}^2}⟹-8x-36=-12\sqrt{{(x-0)}^2+{(y+2)}^2}⟹2x+9=3\sqrt{{(x-0)}^2+{(y+2)}^2}⟹{(2x+9)}^2={\left(3\sqrt{{(x-0)}^2+{(y+2)}^2}\right)}^2⟹9x^2+5y^2=45.⟹ThisisthelocusofP.Ans-OptionC.$