Question

the distance of point P(x , y) from the points A(1 , -3) and B(-2 , 2) are in the ratio 2 : 3. show that : 5x² + 5y² - 34x + 70y + 58 = 0.
(solve the question correctly and I will mark it brainliest)​

Answer 1

Hey mate!!

__________________________________________________________

Let,

AP=2a,

BP=3a

AP = √(x-1)²+(y+3)² =2a

→ x²+1-2x+y²+9+6y=4a². Eqn______(1)

BP= (x+2)²+(y-2)²=9a²

Go through the attachment!!

Hope you get your answer :)

#Jaihind

Answer 2

Distance formula :

$\texttt{Distance between x1,y1 and x2,y2 is given by the formula :}\\\\\mathtt{\sqrt{(x2-x1)^2+(y2-y1)^2}}$

P ( x,y ) ---------- A ( 1, -3 )

P ( x,y ) ---------- B ( -2,2 )

Distance of PA : Distance of PB = 2:3

= 3 Distance PA = 2 Distance PB

$3\sqrt{(x-1)^2+(y+3)^2}=2\sqrt{(x+2)^2+(y-2)^2}\\\\\texttt{Square\:both\:sides}\\\\\implies 9[x^2+1-2x+y^2+9+6y]=4[x^2+4x+4+y^2+4-4y]\\\\\implies 9[x^2+y^2+10-2x+6y]=4[x^2+y^2+4x+8-4y]\\\\\implies 9x^2+9y^2+90-18x+54y=4x^2+4y^2+16x+32-16y\\\\Transpose\:the\:values\:to\:the\:right\\\\\implies 5x^2+5y^2-34x+70y+58=0$

Hence proved !