Show that x2 + y2 - 6x - 9y + 13 = 0, x2 + y2 - 2x - 16y = 0 circles
touch each other. Find the point of contact and the equation of
common tangent at their point of contact.
Answers
Equation of tangent is 4x-7y-13= 0
Point of contact is (5,1). Equation of tangent at point of contact is 7y+13=4x.
1. First solve the two circle equations to form a single line equation. Keep anyone of x or y on one side and the other variables on the other side.
2. Substitute x or y obtained in any one of the circle equations.
3. Solve the equation to obtain the solution. If there are two solutions then the circles intersect, if there is only one solution then the circles touch each other and if there is no solution then the circles doesn't intersect.
4. Substitute the x or y in the line equation obtained in step1. Point of contact is obtained. Using the centres find the slope of tangent and use slope point form of a line to get the tangent equation.
