Question

Find all equations of lines which are tangent to the curve y + 2/(x - 3) = 0 and slope of those is 2.

Answer 1

Putting x = 4 in eq. (i)

y = -2/(4 - 3) = -2

Then, point = (4, – 2)

Again putting, x = 2 in eq. (i)

y = -2/(2 - 3) = 2

Then, point = (2, 2)

Now, tangent at point (4, – 2),

y – (- 2) = 2 (x – 4)

⇒ y + 2 = 2x – 8

⇒ 2x – y – 10 = 0

Again, tangent at point (2, 2),

y – 2 = 2 (x – 2)

⇒ y – 2 = 2x – 4

⇒ 2x – y – 2 = 0

Hence, required equations are 2x – y – 10 = 0 and 2x – y – 2 = 0.