Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

    
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,434 questions

17,804 answers

1,438 comments

60,666 users

Find equations for the tangent line and normal line to the circle at each given point.

0 votes
Find equations for the tangent line and normal line to the circle at each given point. (The normal line at a point is perpendicular to the tangent line at the point.) Use a graphing utility to graph the equation, tangent line, and normal line.

Two circles of radius 4 are tangent to the graph of y^2 = 4x at the point (1, 2). Find equations of these two circles.
asked Jan 22, 2015 in CALCULUS by anonymous

3 Answers

0 votes

Step 1:

The equation is and the point is .

Consider .

Differentiate on each side with respect to .

Slope of the tangent line at .

Slope of the tangent line is .

Step 2:

Point slope form of line equation is image.

Substitute image and in the above equation.

Tangent line is .

Normal line is perpendicular to tangent line then

Slope of tangent line*slope of normal line is equal to .

Point slope form of line equation is image.

Substitute image and in the above equation.

Normal line equation is .

answered Jan 22, 2015 by Lucy Mentor
edited Jan 22, 2015 by Lucy
0 votes

Contd..

Step 3:

Equation of circle with center and radius is .

Differentiate on each side with respect to .

Substitute .

Substitute in the above equation.

Step 4:

Substitute in the circle equation

Circle passes through the point .

Roots of the quadratic equation is .

Then,

Therefore and .

answered Jan 22, 2015 by Lucy Mentor
0 votes

Contd..

Step 5:

Substitute in .

Substitute in .

Circle equations are and

.

Step 6:

Graph.

Graph both the circle equations, curve, tangent line, normal line and point.

image

Solutions:

Tangent line equation is .

Normal line equation is .

Circle equations are and

.

answered Jan 22, 2015 by Lucy Mentor
edited Jan 22, 2015 by Lucy

Related questions

...