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Ludmilka [50]
3 years ago
6

Question 3 (4 MARKS) Find the equation of the tangents to the curve of the function with rule y = x^2 at the points where x = a

and x =-a and find the coordinates of the point of intersection of these two tangents.​
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
3 0

Answer:

(0 , -a²)

Step-by-step explanation:

tangent at x = a and x = -a

y = x²     (a , a²) and (-a , a²) must be on the curve and tangent to curve

gradient dy/dx = 2x

slope (m) at x = a is <u>2a</u>     and slope (m') at x=-a is<u> -2a</u>

line1: (y - a²) / (x - a) = 2a

        y - a² = 2a (x - a)                           y = 2ax - a²   ... (1)

line2: (y - a²) / (x + a) = - 2a                   y = -2ax- a²   ... (2)

(1) - (2): 4ax = 0       a≠0    x = 0

y = - a²

I wish I did it right, or ....

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