Question

A point P is at a distance of√10 from the point 2,3.Find the coordinates of point P if its y coordinate is twice the x coordinate

Answer 1

y = 2x
√(x - 2)^2+ (y - 3)^2 = √10
x^2 + 4 - 4x + 4x^2 + 9 -12x = 10
5x^2 + 13 - 16x =10
5x^2 - 16x = - 3
5x^2 - 16x + 3 = 0
5x^2 - 15x - x + 3 =0
5x(x - 3) - (x - 3) = 0
(5x - 1) (x - 3) = 0
x = 1/5 and 3
if x = 1/5 then y = 2/5
if x = 3 then y = 6

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Answer 2

Answer:

Step-by-step explanation:

y = 2x

√(x - 2)^2+ (y - 3)^2 = √10

x^2 + 4 - 4x + 4x^2 + 9 -12x = 10

5x^2 + 13 - 16x =10

5x^2 - 16x = - 3

5x^2 - 16x + 3 = 0

5x^2 - 15x - x + 3 =0

5x(x - 3) - (x - 3) = 0

(5x - 1) (x - 3) = 0

x = 1/5 and 3

if x = 1/5 then y = 2/5

if x = 3 then y=6