Find the equation of a tangent line to the curve y = x^2 which also passes thru the point (13, 144)...?

Question

A. y = 18x - 81
B. y = -2x - 1
C. y = 4x - 4
D. y = -16x - 64
E. y = 2x - 1
F. y = -50x - 625
G, y = 16x - 64
H. y = -36x - 324
I. none of these

Answer 1

It is G. The slope of the line is (x^2-144)/(x-13) and also is 2x. Make this equation, cross multiply and find that x=8. So the point of tangency is (8,64). That makes its slope 16, and 16(13) - 64 = 144

Answer 2

I won't do the whole problem (although I just solved it myself), but I will get you going so you can finish it yourself.

If you're in a calculus class, you know the derivative (slope) of the parabola is y' = d/dx(x^2) = 2x. So the slope of the line you're looking for is 2x, where x is the point of tangency.

Now suppose the point of tangency is at x = a. Then y = x^2 = a^2, and the full coordinates are (a,a^2). The slope is 2x = 2a.

Now you have two points -- (13,144) and (a,a^2) -- and the slope 2a. Given two points, the slope formula is

(a^2 - 144)/(a - 13) = 2a

Solve this for a. You'll get a quadratic which you can factor, (The point of tangency will be at (a,a^2).)

Once you have a, then plug it into the point-slope formula

(y - 144)/(x - 13) = 2a

Solve for y and that will be the right answer.

Answer 3

hi, to start up, we commit to placed 7x+y=-5 into slope-intercept sort. to attempt this, we commit to isolate y. So: 7x+y=-5 y=-7x-5 Now, utilising the classic formulation of a slope-intercept equation, y=mx+b, wherein m is the slope and b is the y-intercept, all of us understand that the slope of the equation is -7. by technique of the definition of parallel lines, see you later as 2 lines have an similar slope, they're parallel. So all of us understand so a procedures that the slope of this secret line is -7. Now, transferring onto searching the y-intercept, we commit to finish somewhat plugging in. once back, we are going to carry contained in the classic formulation of a slope-intercept equation, y=mx+b. With the given element (a million,2), we can plug those in to their respective x and y values. we may also change -7 for m. y=mx+b 2=-7(a million)+b 2=-7+b 9=b b=9 So now that all of us understand that our y-intercept is 9, we are going to easily finished our equation. y=-7x+9 The equation of a line that passes by potential of the point (a million,2) and is parallel to the line 7x+y=-5 is y=-7x+9. desire I helped! ^_^

Answer 4

y=26x-194

Answer 5

i think the answer is i