# For what values of a and b is the line 5x + y = b tangent to the parabola y = ax^{2} when x = 4?

**Solution:**

Given the line: 5x + y = b.

et us find the slope of the line.

**Step 1:** Differentiate w.r.t ‘x’.

dy/dx = - 5 --------> (1)

Given parabola : y = ax²

Let us find the slope of parabola.

**Step 2: **Differentiate w.r.t ‘x’.

dy/dx = d/dx (ax^{2})

dy/dx = 2ax

At x = 4

dy/dx = 8a --------> (2)

**Step 3: **Equate equation(1) and (2), we get

-5 = 8a

** a = -5/8**

**Step 4: **Substitute the values of a and x in the equation of parabola to get y.

y = (-5/8)(4)^{2}

y = -10

**Step 5: **Substitute the values of a, x and y in the equation of line.

5x + y = b

5(4) + -10 = b

**b = 10**

Thus for a = -5/8 and b = 10 the line 3x + y = b is a tangent to the parabola y = ax²

## For what values of a and b is the line 5x + y = b tangent to the parabola y = ax² when x = 4?

**Summary:**

The line 5x + y = b tangent to the parabola y = ax^{2} when x = 4 has values of a and b are -5/8 and 10 respectively.