Question

if the distance of the point p(x,y) from A(a,0) is a+x then y^2=?
(a 2ax
(c) 4ax
(6) 6ax
(d) 8ax​

Answer 1

Answer:

Step-by-step explanation:

distance between 2 points

√(x-a)^2+(y) ^2=a+x

squaring both sides

(x-a) ^2 -(a+x)^2 +y^2 =0

-4ax+y^2=0

y^2=4ax

proved

Answer 2

Answer:

4ax

Step-by-step explanation:

 From the properties of coordinate axes :

Distance b/w any points is given by √{ ( x₁ - x₂ )^2 + ( y₁ - y₂ )^2 }, where ( x₁ , y₁ ) and ( x₂ , y₂ ) are those points.

  Here,

      Those two points are ( x , y ) and ( a , 0 ). And distance between them is a + x. It means :

⇒ √{ ( a - x )^2 + ( y - 0 )^2 } = a + x

⇒ ( a - x )^2 + y^2 = ( a + x )^2

       Using ( a - b )^2 and ( a + b )^2 = a^2 + b^2 + 2ab and a^2 + b^2 - 2ab ( for solving ( a - x )^2 and ( a + x )^2 )

⇒ a^2 + x^2 - 2ax + y^2 = a^2 + x^2 + 2ax

⇒ - 2ax + y^2 = 2ax

⇒ y^2 = 2ax + 2ax

⇒ y^2 = 4ax

  Hence the required value of y^2 is 4ax.