Distance of points P from origin is 7 units, from x-axis is √13 units and from y-axis is √40 units. Then find the coordinates of point P.
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Let the point A be (x,2x)
Now, using distance formula between (x,2x) and (4,3)
⇒ (4−x) 2 +(3−2x) 2
=10
Squaring both sides we get,
= (4−x)2+(3−2x) 2
=( 10 )2
⇒ 16−8x+x 2 +9−12x+4x 2
=10
⇒ 5x 2 −20x+15=0
⇒ x 2 −4x+3=0
⇒ x 2 −3x−x+3=0
⇒ x(x−3)−1(x−3)=0
⇒ (x−3)(x−1)=0
⇒ x−3=0 and x−1=0
∴ x=3,1
Co-ordinates when x=3
⇒ (x,2x)=(3,6)
Co-ordinates when x=1
⇒ (x,2x)=(1,2)
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