Find the y-intercept of the tangent line to the curve y=sqrt(x^2+33).

The answer is 33/7.

Find the y-intercept of the tangent line to the curve y=sqrt(x^2+33).

The answer is 33/7.

Tutors, please sign in to answer this question.

Westford, MA

Find the y-intercept of the tangent line to the curve y=sqrt(x^2+33). The answer is 33/7.

You neglected to tell us what point on the curve the tangent line intersects. Since you did give us the y-intercept of the tangent line, let's find the point(s).

y=sqrt(x^2+33)

y' = x/sqrt(x^2+33) = x/y

Assume the point(s) on the curve where the tangent line(s) intersect are (p,q).

q= y(p) = sqrt(p^2+33)

Equation of tangent line(s) is: y - q = (p/q) * (x - p)

Or: y = (p/q) * x + q - (p/q) * p

The y-intercept = q - p^2/q = 33/7

(q^2 - p^2)/q = 33/7

(p^2 + 33 - p^2)/sqrt(p^2+33) = 33/7

Numerators are the same so denominators are equal:

sqrt(p^2+33) = 7

Square both sides:

p^2 + 33 = 49

p^2 = 16

p = ±4

q = sqrt((±4)^2+33) = 7

So tangent lines at either of the two points (±4,7) have the same y-intercept = 33/7.

Dana R.

English/Math SAT PrepTutor with PhD

Lynbrook, NY

4.8
(85 ratings)

Andrea R.

Ph.D. Tutor: K-9 Reading, Math, Writing, Test Prep, Special Needs

Wyckoff, NJ

5.0
(408 ratings)

Michael E.

H.S. Mathematics Tutor (Certified NJ Teacher)

Saddle Brook, NJ

5.0
(113 ratings)

- Math 8574
- Math Word Problem 3833
- Math Help For College 1301
- Math Problem 913
- Math Equations 923
- Math Question 722
- Word Problem 4716
- Algebra 4546
- Algebra 2 3147
- Algebra Help 938

## Comments