# The equation of the parabola ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 3.1, Problem 65E
To determine

## To find:The equation of the parabola

Expert Solution

The equation of the parabola is y=2x2x

### Explanation of Solution

Given:

The normal line to the parabola

y=ax2+bx

Concept used:

The equation is in slope −intercept form, y=mx+c

An equation for the line through the point (x1,y1) with slope m is

yy1=m(xx1)

Calculation:

The function

y=ax2+bx.......................(1)

The derivative of a function

y=f(x)y=f(x)=dydx=m

Differentiating the equation (1) with respect to x

y=ax2+bxy=2ax+b........................(2)

The slope of the tangent

m=2a(1)+bm=2a+b

Point (1,1) is a point on the parabola

So, satisfies the original parabola equation

1=a(1)2+b(1)a+b=1

The line intersect the parabolas

2a+b=3a+b=1solvea=2a+b=1b=1

So parabola equation is

y=ax2+bxy=2x2x

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