Question

The slope of the tangent to a curve at any point (x, y) on the curve is x/y . Find the equation of the curve if the point (2, -3) is on the curve.

Answer 1

I got x^2 + y^2 = 13

Answer 2

let equation of tangent =>
y = mx +c
given slope = x/y at point (x,y)

so eq => y = (x/y)*x +c
point ((2, -3)) is on this line

insert (2, -3) in place of x,y find c

Answer 3

x^2-y^2=a^2
2^2+3^2=a^2
13=a^2
x^2 + y^2 = 13

Answer 4

were you able to find small c

Answer 5

hold on. your c will be -5/3

and equation will be y^2 = x^2 -3*5/(-3) = y^2 = x^2 +5

Answer 6

ohhh ok so my answer would be x^2-y^2=5

Answer 7

y^2-x^2 = 5

Answer 8

thank you!!