SOLUTION: Find the equation of the tangent to the curve (x-3)^2+(y+2)^2=25 at the point on the curve, in the fourth quadrant, where x=7. I've already solved for the formula, but how do you f

Algebra.Com
Question 608398: Find the equation of the tangent to the curve (x-3)^2+(y+2)^2=25 at the point on the curve, in the fourth quadrant, where x=7. I've already solved for the formula, but how do you find the y value for where x=7? Do you have to use the distance formula from the C(3,-2) to P(7, y) and solve for y or what? I'm confused. D:
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
Find the equation of the tangent to the curve (x-3)^2+(y+2)^2=25 at the point on the curve, in the fourth quadrant, where x=7.
**
Find y using equation of curve (circle)
Plug in 7 for x
(7-3)^2+(y+2)^2=25
(4)^2+(y+2)^2=25
16+(y+2)^2=25
(y+2)^2=25-16=9
take sort of both sides
y+2=±√9=±3
y=-2±3
y=-5
or
y=1 (not in 4th quadrant, so y=-5)
Point of tangency: (7,-5)
..
Finding slope of line tangent to circle at (7,-5)
This line is perpendicular to the line connecting center of circle(3,-2) to point of tangency (7,-5)
So its slope is the negative reciprocal of the tangent line slope.
slope of perpendicular line=change in y/change in x=∆y/∆x=(-2-(-5))/(3-7)=-3/4
slope of tangent line=4/3
Equation of line: y=mx+b, m=slope, b=y-intercept
y=4x/3+b
solve for b using coordinates of point of tangency(7,-5)
-5=4*7/3+b
b=-43/3
equation of line tangent to circle where x=7: y=4x/3-43/3
..


RELATED QUESTIONS

find where the tangent to the curve y=x^3 at the point where x=2, meets the curve... (answered by greenestamps)
The equation of a curve is y = x^2/(x+2). The tangent to the curve at the point where x = (answered by MathLover1)
Find the equations of the tangents to the curve y = x^3 - x^2 - 2 at the point where x =... (answered by josgarithmetic)
Find the equation of the tangent line to the curve {{{(x-y)^2}}}{{{""=""}}}{{{2x+1}}}... (answered by Edwin McCravy)
Find the equation of the tangent line to the curve (x-y)^2=2x+1 at the point... (answered by Alan3354)
Find the equation of the tangent line to the curve (x-y)^2=2x+1 at the point... (answered by Fombitz)
A curve is given: y = e^-x^2. Find the point on the curve where the slope of the tangent... (answered by Fombitz)
(a) use the method of first principal of differentiation to find the derivative of... (answered by Boreal,solver91311)
Find the equation of the tangent to the curve y=x+x^2 at the point where x=a find the... (answered by ikleyn,greenestamps)