Chapter 6.3, Problem 2PSA

To determine

To verify: The point (3, 4) is on the circle, that is the graph of the equation ${\text{x}}^2+{\text{y}}^2=25$

Explanation of Solution

Given information:

Equation of the circle ${\text{x}}^2+{\text{y}}^2=25$

And a point D (3, 4)

Formula used:

Substitution method

Proof:

Point D is given as (3, 4)

For verification,

Put x = 3 and y = 4 in the equation of circle

Given equation of circle

  ${\text{x}}^2+{\text{y}}^2=25$

We get

Left side of the equation

  $\begin{array}{l}{\text{=x}}^2+{\text{y}}^2\\ =3^2+4^2\\ =9+16\\ =25\end{array}$

Which is right side of the equation

Hence verified