# calc

standard equation of circle concentric with X^2+Y^2-2X-8Y+1=0 and tangent to line 2X-Y=3

Complete the squares to find the center of the circle.
X^2+Y^2-2X-8Y+1=0
(x-1)^2+(y-4)^2 - 16 =0
The center is (1,4) and the radius for the given circle is 4.
Now find the distance from (1,4) to the line to get the radius, then write the concentric circle's equation.

how do I get the distance if I don't have a point of intersection with the line or do I?

If you have a point (x1,y1), the distance to the line Ax+By+C=0 is
|Ax1+By1+c|/sqrt(A^2+B^2)
No, you don't have a point of intersection, you just want to find the distance and use that for the radius. The circle and line need to be tangent.

Thank you so much...

1. 👍
2. 👎
3. 👁
1. just believe in god

1. 👍
2. 👎

## Similar Questions

1. ### GEOMETRY INSCRIBED ANGLES MULTIPLE CHOICE QUESTION

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. {THe figure is a circle with a tangent crossing through the top section of the circle. The value of the tangent is 12.

2. ### Calculus

1. use the definition mtan=(f(x)-f(x))/(x-a) to find the SLOPE of the line tangent to the graph of f at P. 2. Determine an equation of the tangent line at P. 3. Given 1 & 2, how would I plot the graph of f and the tangent line at

3. ### Math (Calculus) (mean value theorem emergency)

Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c

4. ### Math

The point P = (4, 3) lies on the circle x2 + y2 = 25. Find an equation for the line that is tangent to the circle at P. This line meets the x-axis at a point Q. Find an equation for the other line through Q that is tangent to the

1. ### Math

A tangent is a line that touches a circle at exactly one point. For what values of k will the line y= x+k be tangent to the circle x^2+ y^2 = 25? I know I'm suppose to use the properties of a discrimminate. But how

2. ### GEOMETRY INSCRIBED ANGLES MULTIPLE CHOICE QUESTION

segment BC is tangent to circle A at B and to circle D at C. (Not drawn to scale) AB=10 BC=25 and DC=3. Find AD to the nearest tenth. Hint: Draw an auxiliary line from D to segment BA. {There are two circles, the larger one has

Suppose that the area between a pair of concentric circles is 49pi. Find the length of a chord in the larger circle that is tangent to the smaller circle.

4. ### math

Find an equation of the circle Center on line y–4=0, tangent x-axis at (–2, 0)

1. ### Math

If the equation of the circle is x^2 + y^2 = r^2 and the equation of the tangent line is y =mx + b, show that the point of tangency is (-r^2m/b , r^2/b)

2. ### Math (geometry)

Line l is tangent to circle O at point P(3,4) where the center is located at (0,0). a. Find the radius of the circle. (I got 4) b. Give an equation of the circle. (I got x^2+y^2=16) c. Find the slope of line l. d. Give an equation

3. ### Calculus

Find the equation of a circle with center C(1,6) and tangent line x-y-1=0.