Thursday
May 23, 2013

# Homework Help: math

Posted by David on Wednesday, October 14, 2009 at 7:25pm.

Two circles of radius 4 are tangent to the graph y^2=4x at the point (1,2). Find the equations of the two circles.

• math - MathMate, Wednesday, October 14, 2009 at 8:23pm

The given parabola y²=4x has the axis along the x-axis. So we will work with its inverse, y=2√x. The slope can be obtained by differentiation, dy/dx = 1/sqrt(x).
The slope of the tangent line at (1,2) is therefore 1/sqrt(1) = 1
The slope of the normal, N0, to the curve at this point is m=1/(-1) = -1
(y-y1)=m(x-x1), substituting m=-1, x1=1, y1=2 the normal is

N0 : y = -x +3

Since both required circles pass through (1,2), their centres will be on the circumference of a circle C0 with radius 4 centred on the point of tangency, where

C0 : (x-1)² + (y-2)² = 4²

The centres of the required circles will be found at the intersections of N0 and C0.

Can you take it from here?

Related Questions

math - Two circles of radius 4 are tangent to the graph of y^2=4x at the point (...
maths - there are two circles touching each other at one point. The radius of ...
Geometry - Circles and tangents - Two circles of radius 1 are externally tangent...
calculus - if the tangent of two intersecting circles, at their points of ...
GEOMETRY(CIRCLE) - Three circles with different radii have their centers on a ...
8th grade Math - This four-leaf clover consists of four coplanar circles. Each ...
Math - Circle C has radius 4 inches. Circle D had radius 9 inches. These two ...
geometry - Three circles are externally tangent to one another. The radius of ...
Math. Help me please! - The two circles have equations x^ + (y-3)^2 = 49 and x^2...

Search
Members
Community
FEATURES