Question

Find The Equation of Tangent to parabola of y^2=24x and having slope 3/2​

Answer 1

Answer:

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Answer 2

Equation of tangent is $\bf \: 3x - 2y + 8 = 0$

Given:

• A parabola ${y}^{2} = 24x$
• Slope of tangent 3/2.

To find:

• Find the equation of tangent.

Solution:

Formula to be used:

• Equation of line passes through (x1, y1) having slope m is $\bf (y - y1) = m(x - x1)$
• Slope of tangent on curve $\bf m = \frac{dy}{dx}$

Step 1:

Differentiate curve with respect to x.

$\frac{d}{dx} ( {y)}^{2} = \frac{d}{dx}(24x)$

or

$2y \frac{dy}{dx} = 24$

or

$\bf \frac{dy}{dx} = \frac{12}{y} ...eq1$

Step 2:

Equate slope of tangent and eq1.

$\frac{12}{y} = \frac{3}{2}$

or

$\bf y = 8$

put the value of y in curve.

$( {8)}^{2} = 24x$

or

$x = \frac{64}{24}$

or

$\bf x = \frac{8}{3}$

Thus,

The point is (8/3,8)

Step 3:

Find the equation of tangent.

It passes through (8/3,8) having slope 3/2.

Equation of tangent:

$y - 8 = \frac{3}{2} (x - \frac{8}{3} )$

or

$2y - 16 = 3x - 8$

or

$- 3x + 2y = - 8 + 16$

or

$3x - 2y + 8 = 0$

Thus,

Equation of tangent is $\bf \: 3x - 2y + 8 = 0$

Learn more:

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