If θ denotes the acute angle between the curves, y = 10 - x2 and y = 2 + x2 at a point of their intersection, then | tan θ | is equal to :

Question

If θ denotes the acute angle between the curves, y = 10 - x2 and y = 2 + x2 at a point of their intersection, then | tan θ | is equal to : (A) 4/9 (B) 7/17 (C) 8/17 (D) 8/15

Tardigrade Admin · Accepted Answer

Point of intersection is P(2,6). Also, m1 = ((dy/dx))P(2,6) = - 2x - 4 m2 =((dy/dx))P(2,6) = 2x=4 ∴ | tanθ| = |(m1 -m2/1+m1m2)| = (8/15)

Q. If $θ$ denotes the acute angle between the curves, $y = 10 - x^{2}$ and $y = 2 + x^{2}$ at a point of their intersection, then $∣ tan θ ∣$ is equal to :

$4/9$

$7/17$

$8/17$

$8/15$

Point of intersection is $P (2, 6)$ .
Also, $m_{1} = (\frac{d y}{d x})_{P (2, 6)} = - 2 x - 4$
$m_{2} = (\frac{d y}{d x})_{P (2, 6)} = 2 x = 4$
$∴ ∣ tan θ ∣ = ∣ ∣ \frac{m _{1} - m _{2}}{1 + m _{1} m _{2}} ∣ ∣ = \frac{8}{15}$

Q. If θ denotes the acute angle between the curves, y=10−x2 and y=2+x2 at a point of their intersection, then ∣tanθ∣ is equal to :

4/9

7/17

8/17

8/15