Answer to Question #221033 in Math for Chrissy

Question

Consider the graph G of the function f(x) =x^ 2 and the point M(5,2) on the Cartesian plane.

(a)Find the coordinates of a point A on Gand a point B on x-axis, given that M(5,2)is the midpoint of the line segment [AB].

(b) Find the coordinates of a point C on G, given that the distance between M and C is 23

Answer 1

(a)

$$\dfrac{x_A+x_B}{2}=5$$

$$\dfrac{y_A+y_B}{2}=2$$

$$x_A+x_B=10$$

$$x_A^2+0=4$$

$$x_A=-2, x_B=12$$

$$A(-2,4), B(12,0)$$

$$x_A=2, x_B=8$$

$$A(2,4), B(8,0)$$

(b)

$$(x_C-5)^2+(y_C-2)^2=23^2$$

$$y_C=x_C^2$$

$$x_C^2-10x_C+25+x_C^4-4x_C^2+4=529$$

$$x_C^4-3x_C^2-10x_C-500=0$$

$$(x_C-5)(x_C^3+5x_C^2+22x_C+100)=0$$

$$x_C=5, y_C=25$$

$$C(5, 25)$$

$$x_C\approx-4.777, y_C\approx22.820$$

$$C(-4.777,22.820)$$