Write the equation of the circle in standard form if the points (3,5) and (-5,-1) are endpoints of the diameter

The equation of the circle in standard form if the points (3,5) and (-5,-1) are endpoints of the diameter is

Step-by-step explanation:

Let AB be the Diameter and the end points be

point A( x₁ , y₁) ≡ ( 3 , 5)

point B( x₂ , y₂) ≡ (-5 , -1)

A circle is given as AB is a Diameter.

To Find:

Equation of the circle in standard form = ?

Solution:

Diameter form of the equation of the circle is

(x - x₁)(x - x₂) + (y - y₁)(y - y₂ ) = 0

Where ( x₁ , y₁) and ( x₂ , y₂) are the endpoints of the diameter.

So on substituting the value we get the required equation of circle

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

∴ (x - 3)(x + 5) + (y - 5)(y + 1) = 0

Applying Distributive property we get

The equation of the circle in standard form if the points (3,5) and (-5,-1) are endpoints of the diameter is

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

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