Q: When you're trying to determine whether a sentence is parallel or not, try isolating each individual element. Then, rewrite the sentence with only that section.  For instance, in our previous example,  “Kate is fast, efficiently, and courteous,” both the sentences “Kate is fast,” and “Kate is courteous,” make perfect sense, since they have a subject, a verb, and an adjective. However, the sentence “Kate is efficiently,” doesn’t make sense, since "efficiently" is an adverb. The simplest way to fix this sentence to change the adverb “efficiently” to the adjective “efficient.” Since “Kate is efficient,” is grammatically correct, you know that “Kate is fast, efficient, and courteous,” is a parallel sentence. When you’re listing a series of similar items, especially infinitive verbs, you may notice some repetition, particularly of the word “to.” It’s up to you whether to leave the repetition in place, but removing it can make your writing seem more streamlined.The sentence, "He likes to run, to dance, and to sing,” is correct, since the verbs are all infinitives, but “He likes to run, dance, and sing,” is more to the point.
A: Isolate each part of the sentence if you're not sure if it's correct. Omit repeated words in a series to make your writing more concise.

Q: We'll start with a simple example: a hyperbola with the center of its origin. For these hyperbolas, the standard form of the equation is x2/a2 - y2/b2 = 1 for hyperbolas that extend right and left, or y2/b2 - x2/a2 = 1 for hyperbolas that extend up and down. Remember, x and y are variables, while a and b are constants (ordinary numbers).   Example 1: x2/9 - y2/16 = 1  Some textbooks and teachers switch the position of a and b in these equations. Follow the equation closely so you understand what's going on. If you just memorize the equations you won't be prepared when you see a different notation. This new equation represents both asymptotes, though it will take a little more work to separate them.  Example 1: x2/9 - y2/16 = 0 Factor the left hand side of the equation into two products. Refresh your memory on factoring a quadratic if you need to, or follow along while we continue Example 1:  We'll end up with an equation in the form (__ ± __)(__ ± __) = 0.  The first two terms need to multiply together to make x2/9, so take the square root and write it in those spaces: (x/3 ± __)(x/3 ± __) = 0  Similarly, take the square root of y2/16 and place it in the two remaining spaces: (x/3 ± y/4)(x/3 ± y/4) = 0  Since there are no other terms, write one plus sign and one minus sign so the other terms cancel when multiplied: (x/3 + y/4)(x/3 - y/4) = 0 To get the equations for the asymptotes, separate the two factors and solve in terms of y.   Example 1: Since (x/3 + y/4)(x/3 - y/4) = 0, we know x/3 + y/4 = 0 and x/3 - y/4 = 0  Rewrite x/3 + y/4 = 0 → y/4 = - x/3 → y = - 4x/3  Rewrite x/3 - y/4 = 0 → - y/4 = - x/3 → y = 4x/3 We've just found the asymptotes for a hyperbola centered at the origin. A hyperbola centered at (h,k) has an equation in the form (x - h)2/a2 - (y - k)2/b2 = 1, or in the form (y - k)2/b2 - (x - h)2/a2 = 1. You can solve these with exactly the same factoring method described above. Just leave the (x - h) and (y - k) terms intact until the last step.   Example 2: (x - 3)2/4 - (y + 1)2/25 = 1  Set this equal to 0 and factor to get: ((x - 3)/2 + (y + 1)/5)((x - 3)/2 - (y + 1)/5) = 0 Separate each factor and solve to find the equations of the asymptotes: (x - 3)/2 + (y + 1)/5 = 0 → y = -5/2x + 13/2 ((x - 3)/2 - (y + 1)/5) = 0 → y = 5/2x - 17/2
A: Write down the equation of the hyperbola in its standard form. Set the equation equal to zero instead of one. Factor the new equation. Separate the factors and solve for y. Try the same process with a harder equation.

Q: It's a round icon depicting a fox curled around a globe.  Firefox will open a dialog box, then automatically check for and download any available updates. The updates will be installed when Firefox relaunches.
A:
Open the Firefox app. Click on the ☰ icon and select Help from the dop-down list. Click on About Firefox. Click on Restart Firefox to Update in the dialog box.