Question

M(4,3) Figure 2 Figure 2 above shows a sketch of the circles $C_1$ and $C_2$. The circle $C_1$ has the equation $x^2 + y^2 = 4$. The circle $C_2$ has centre M(4, 3) and touches $C_1$ externally, as shown in the figure. (a) Show that the radius of $C_2$ is 3.

          M(4,3)
Figure 2
Figure 2 above shows a sketch of the circles $C_1$ and $C_2$.
The circle $C_1$ has the equation $x^2 + y^2 = 4$.
The circle $C_2$ has centre M(4, 3) and touches $C_1$ externally, as shown in the figure.
(a) Show that the radius of $C_2$ is 3.

M(4,3)
Figure 2
Figure 2 above shows a sketch of the circles C1 and C2.
The circle C1 has the equation x^2 + y^2 = 4.
The circle C2 has centre M(4, 3) and touches C1 externally, as shown in the figure.
(a) Show that the radius of C2 is 3.

Added by Jeremy R.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Maria Dearborn

08/31/2023

Step 1

x^2 + y^2 - 4x + 6y - 12 = 0 Rearranging the terms: (x^2 - 4x) + (y^2 + 6y) = 12 To complete the square for x, we need to add (4/2)^2 = 4 to both sides: (x^2 - 4x + 4) + (y^2 + 6y) = 12 + 4 (x - 2)^2 + (y^2 + 6y) = 16 To complete the square for y, we need Show more…

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Figure Sketch of the circles â‚¬ and Cz" shown in Figure 1. The circle â‚¬ has the equation x^2 + y^2 - 4x + 6y - 12 = 0. The circle Cz has center M(4,3) and radius 4. (a) Show that the radius of circle â‚¬ is 2.