Imagine we drew a line from the centre (2,0) to the point (0,4).
Essentially the line<u> we drew from the centre to that point on the circle is perpendicular to the tangent line slope-wise</u>.
The <u>slope of that line from the centre to the point is -2</u> based on the slope's equation or formula.
slope = 
Therefore the <u>tangent equation's slope is 1/2</u> since any perpendicular line's slope is the negative reciprocal of the original line's slope.
By<u> using the point-slope form, we must have the point on the tangent plane (0,4) and the slope we found which is 1/2</u>.

Hope that helps!
Answer:
All squares have four equal angles
Step-by-step explanation:
Every square must have four equal angles to be a square
The Standard form of the equation of circle is (x+21)² + (y+19)² = 849
<h3>What is Standard form of circle?</h3>
To transform general form to a standard form, you can use completing the square method or you can convert this equation
x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0
Here, Given: x² + y² + 42x + 38y − 47 = 0
Required: Find the values of h, k, and r using this formula
x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0
On comparing we get,
-2h = 42
h = 21
-2k = 38
k = 19
-47 = h² + k² - r²
-47 = 21² + 19² - r²
r² = 849
r = √849
Thus, the Standard form of the equation of circle is (x+21)² + (y+19)² = 849
Learn more about Circle from:
brainly.com/question/11833983
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