Question

The tangent to the parabola x2 = 2y at the point (1, 12) makes with the x-axis an angle

of

(a) 0° (b) 45° (c) 30° (d) 60°​

Answer 1

Answer:

45°

Step-by-step explanation:

Given $x^{2}$=2y

⇒y= $\frac{1}{2} x^{2}$

⇒ $\frac{dx}{dy}$ = x.

∴ Slope of tangent at (1, $\frac{1}{2}$)=1.

Hence, required angle is 45°.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The tangent to the parabola x² = 2y at the point (1, 1/2) makes with the x-axis an angle of

(a) 0°

(b) 45°

(c) 30°

(d) 60°

EVALUATION

Here the given equation of the parabola is

x² = 2y

Differentiating both sides with respect to x we get

$\displaystyle \sf{2x = 2 \frac{dy}{dx} }$

$\displaystyle \sf{ \frac{dy}{dx} = x }$

$\displaystyle \sf{ \frac{dy}{dx} \bigg| _{(1, \frac{1}{2} )}= 1 }$

Let the tangent to the parabola x² = 2y at the point (1, 1/2) makes an angle θ with the x-axis

Then

tan θ = 1

⇒ θ = 45°

Thus the required angle

FINAL ANSWER

Hence the correct option is (b) 45°

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