Graph the circle (x+2)^2 + (y-1)^2= 25
1. It is a circle with the centre C(-2, 1) and the radius 5.
2. The radius is perpendicular to the tangent in the tangent point. Thus the radius has the slope -4/3 and has to pass the centre:
Calculate the intersection of this line and the circle and you'll get the tangent points:
. After a few transformation you get:
. Solve for x. Plug in the values into the equation of the straight line r. The tangent points are:
3. You know the slope of the tangent and one point of the tangent. Use the point-slope-formula.
here is another approach:
You allways find 2 parallel tangents to a circle. The equation of these tangents differ only in the constant summand. With your values the tangents have the form:
Now calculate the intersection points of these tangents and the circle. Plug in the tangent term into the equation of the circle:
. Expand the brackets and after a few steps you'll get the equation:
. Solve for x:
You get only one intersetion point (that is the tangent point) if the radicand equals zero:
. Solve for C. You'll get:
Plug in this value into the equation of the parallel lines and you have the result you know from my previous post.
in my previous post I mentioned that the centre of the circle is C(-2, 1) and the radius is 5. I have some difficulties to imagine what difficulties you could have to draw a circle if all data are present
But nevertheles here it is:
By the way: Don't delete your problem when you have received an answer. Other members of the forum could benefit from your problem and the way it is solved.