Question

any line is said to be a tangent to the curve, if it intersects the curve at one point. if the line y=kx-3is a tangent to the curve y=2x^2+7 then the possiblevalues of k are

Answer 1

Answer:

any line is said to be a tangent to the curve, if it intersects the curve at one point. if the line y=kx-3is a tangent to the curve y=2x^2+7 then the possiblevalues of k are

Answer:

Answer 2

Answer:

The possible values of k are ±4√5.

Step-by-step explanation:

• If the line y = kx - 3 is a tangent to the curve of the function y = 2$x^{2}$ + 7, then they meet in one point (x, y).

Now,

2$x^{2}$  + 7 = kx - 3

⇒ 2$x^{2}$ - kx + 10 = 0 ....................................................(i)

a$x^{2}$ + bx + c = 0.....................................................(ii)

Comparing (i) and (ii), we can write

where a = 2, b = -(k), c = 10

we know that , $b^{2}$ - 4ac = 0

Therefore: $(-k)^{2}$ - 4 ×2 × 10 = 0

⇒$k^{2}$-80 = 0

⇒ $k^{2}$ =±√80

⇒ k = ±4√5