write the standard form of the equation of the parabola with the following A) Center (0,0) and r=7 B) Center (-3,2) and r =5

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You should remember what is the standard form of equation of the circle such that:

`(x-h)^2+(y-k)^2=r^2`

Notice that (h,k) represents the center of circle and r represents the radius.

Since the problem provides the coordinates of the center and the value of radius, you just need to substitute these values in standard form of equation of circle such that:

`(x-(-3))^2+(y-2)^2=5^2`

`(x+3)^2+(y-2)^2=25`

Hence, evaluating the standard form of equation of the circle, whose center is at (-3,2) and its radius is of 5, yields `(x+3)^2+(y-2)^2=25.`

Approved by eNotes Editorial Team

Posted on

An illustration of the letter 'A' in a speech bubbles

A parabola can be written as

`(y-y_0) = (x-x_0)^2/(2r)`

where `(x_0,y_0)` is it's centre, or vertex and `r` is the radius of curvature at the centre (twice the focal length).

In standard form a parabola is written as

`y = ax^2 + bx + c`

A) `(y-0) = (x-0)^2/7`  `implies`  `y = x^2/7`

B) `(y-2) = (x-(-3))^2/5`  `implies`  `y = (x+3)^2/5 + 2`

 `implies `  `y = 1/5(x^2 + 6x + 9) + 2`

`implies`  `y = 1/5x^2 + 6/5x + (9+10)/5 = 1/5x^2 + 6/5x + 19/5` ` `

A) y = x^2/7

B) y = 1/5x^2 + 6/5x+ 19/5

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial