Show that two circles S1: x2 + y2 - 4x + 2y + 1 = 0 and S2: x2 + y2 + 2x - 2y + 1 = 0 touch externally and find the equation of their common tangent T at the point of contact.

Question

Asked on May 4, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-05-04T09:03:39.670Z

Welcome back Che — been a while! Let's pick up where you left off. --- Question 9: a) The equations of two circles S_1 and S_2 are given by S_1: x^2 + y^2 - 4x + 2y + 1 = 0 and S_2: x^2 + y^2 + 2x - 2y + 1 = 0. Show that S_1 and S_2 touch externally and obtain the equation of the common tangent T at the point of contact. Step 1: Find the centers and radii of the circles. The general equation of a circle is $x^2 + y^2

Accepted Answer · 2026-05-04T09:03:39.670Z

Welcome back Che — been a while! Let's pick up where you left off. --- Question 9: a) The equations of two circles S_1 and S_2 are given by S_1: x^2 + y^2 - 4x + 2y + 1 = 0 and S_2: x^2 + y^2 + 2x - 2y + 1 = 0. Show that S_1 and S_2 touch externally and obtain the equation of the common tangent T at the point of contact. Step 1: Find the centers and radii of the circles. The general equation of a circle is $x^2 + y^2

Show that two circles S1: x2 + y2 - 4x + 2y + 1 = 0 and S2: x2 + y2 + 2x - 2y + 1 = 0 touch externally and find the equation of their common tangent T at the point of contact.

Need help with your own homework?

More Mathematics Questions

Show that two circles S1: x2 + y2 - 4x + 2y + 1 = 0 and S2: x2 + y2 + 2x - 2y + 1 = 0 touch externally and find the equation of their common tangent T at the point of contact.

Need help with your own homework?

More Mathematics Questions