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)

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

$y_C=x_C^2$

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

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

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

$x_C=5, y_C=25$

$C(5, 25)$

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

$C(-4.777,22.820)$