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EXPLANATION.

Equation of those tangent to the circle x² + y² - 2x - 4y - 4 = 0.

Parallel to the line 3x - 4y - 1 = 0.

As we know that,

General equation of circle.

⇒ x² + y² + 2gx + 2fy + c = 0.

Centre of circle : (-g, -f).

Radius of circle : √g² + f² - c.

Using this concept in this equation, we get.

Centre of the circle : (1, 2).

Radius of the circle : √1² + 2² -(-4).

Radius of the circle : √(1 + 4 + 4).

Radius of the circle : √9.

Radius of the circle : 3 units.

As we know that,

Slope of parallel line : ax + by +c ⇒ -b/a.

Slope of line : 3x - 4y - 1 = 0 ⇒ (-3/-4).

Slope of line : 3/4 = m.

Slope form : From conditions of tangency for every value of m, the line : y = mx ± a√1 + m² is a tangent of the circle x² + y² = a².

Using this concept in this question, we get.

⇒ y = mx ± a√1 + m².

⇒ (y - 2) = 3/4(x - 1) ± 3√[1 + (3/4)²].

⇒ (y - 2) = 3/4(x - 1) ± 3√[1 + 9/16].

⇒ (y - 2) = 3/4(x - 1) ± 3√(16 + 9)/(16).

⇒ (y - 2) = 3/4(x - 1) ± 3√(25/16).

⇒ (y - 2) = 3/4(x - 1) ± 3(5/4).

⇒ (y - 2) = 3/4(x - 1) ± (15/4).

⇒ (y - 2) = 3/4(x - 1) + (15/4).

⇒ 4(y - 2) = 3(x - 1) + 15.

⇒ 4y - 8 = 3x - 3 + 15.

⇒ 4y - 8 = 3x + 12.

⇒ 3x + 12 - 4y + 8 = 0.

⇒ 3x - 4y + 20 = 0.

⇒ (y - 2) = 3/4(x - 1) - (15/4).

⇒ 4(y - 2) = 3(x - 1) - 15.

⇒ 4y - 8 = 3x - 3 - 15.

⇒ 4y - 8 = 3x - 18.

⇒ 3x - 18 - 4y + 8 = 0.

⇒ 3x - 4y - 10 = 0.

Equation of tangents : 3x - 4y + 20 = 0  and  3x - 4y - 10 = 0.

Step-by-step explanation:

Melting glaciers add to rising sea levels, which in turn increases coastal erosion and elevates storm surge as warming air and ocean temperatures create more frequent and intense coastal storms like hurricanes and typhoons.

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